## Non Work Activities Are Known In Economics Assignment

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Choose a grading policy

You can create custom policies to use in your course, or use one of the five built-in policy sets. Click on an assignment on your main course page to view it in the activity editor. In the **Settings** panel, you can see which policy set is active. Click the edit settings button in the **Settings** panel to change the policy. If you do not see the **Settings** panel, you may need to first close the library by clicking the book icon. To edit the policy for several assignments at once, use the Activities and Due Dates page.

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## Built-In policy sets to choose from

Five built-in policy sets are available.

**Homework**: The default policy for new activities is called Homework, and is what we recommend for standard homework assignments. This policy set gives students feedback for their incorrect answers, and allows them to see the solution when they've finished the question. This policy set also includes a built-in calculator and periodic table, and allows students to print assignments. Students are allowed unlimited attempts at Homework assignments, and lose 5% of the available points on each question for each incorrect attempt.**Homework (no periodic table)**: Same as above but removes the periodic table link from assignments. This is typically used for economics or non-science courses.**Practice**: A few of your assignments may be set to Practice mode. Practice mode is identical to Homework mode, except there is no penalty for incorrect attempts. We recommend this policy for assignments that teach students how to use the system since some of those questions may instruct them to get things wrong.**Test**: In Test mode, students do not receive any feedback while they take an assignment and they do not have a**Check Answer**button. They can move back and forth through the assignment, changing their answers as often as they like, but they do not receive any feedback or information about which questions are right or wrong until the due date passes. Students only receive credit in Test mode for their final answers, but all responses are saved.**Practice Test**: Practice Tests are like tests, but students can submit the assignment when they finish to receive feedback immediately about their score.

Custom policies

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If you decide to set a custom policy, you can choose from several settings:

**Name**: Give the policy set a unique name, so you can find it and use it again for another assignment. Adding a space to the end of an existing policy name (e.g. "Homework ") does not create a unique policy name.**Show Feedback**: If this option is checked, students have a**Check Answer**button. When unchecked, you must set the number of attempts to "unlimited" and the percent deduction to "none" because these settings are no longer applicable in the absence of a Check Answer button. Unchecking also removes the feedback and hint from each question.**Show Periodic Table**: Make an interactive periodic table available through a link at the top of the assignment.**Show Calculator**: Make a scientific calculator available through a link at the top of the assignment.**Print**: Allow students to print the assignment to work on it offline. If unchecked, you will also be unable to print the assignment as an instructor (printing is done in student view).**Show Resources (if enabled for this course)**: Resources are helpful information, such as relevant video lectures or textbook sections.**Attempt Deduction for Multiple Choice**: This settings only affects how multiple choice questions are graded. Choosing this option overrides the normal attempt deduction and grades more harshly depending on the number of choices. For example, with 4 choices, it will deduct 33% of the available points per attempt. In most cases, we do not recommend this setting because it does not behave properly for multiple-select questions.**Randomize Question Order**: If this setting is on, each student will receive the assignment questions in a random order.**Guided Solution**: Some questions have special Guided Solution tutorials, which walk students through the question. If this setting is on (recommended for multi-attempt assignments), students will receive a new version of the "main" question after completing a Guided Solution, allowing them to possibly receive full points if they can then answer the question without help.**Timed:**Limit the time a student can spend working on an assignment, but still allow them to start the assignment any time within a larger time frame. For more info, see the help article Timed Assignments.**Number of Attempts**: Set how many times your students can attempt to answer each question (unlimited by default in Homework and Practice modes, 1 in Test modes). Percent deductions, feedback, and guided solutions are not compatible with single-attempt assignments. We recommend allowing at least 4 attempts.**Percent Deduction per Attempt**: Set what percentage of their total score for that question a student will lose for each attempt (5% by default in Homework mode). Set this to "None" for practice assignments**Show Solution:**This policy determines when students can see the solutions to questions:**Upon Completion of each Question**: Reveal solutions when the student gets the correct answer or gives up on each question. This setting adds a**Give Up & View Solution**button to allow students to indicate that they wish to forfeit further attempts and see the answer to the question.**Upon Assignment Completion**: Reveal solutions when the student completes the assignment or the due date passes, whichever comes first. Prior to the due date, a student can "complete" the assignment in one of two ways: (1) they can get all questions correct or (2) they can click the**Submit**button to give up on on any remaining questions. Note that once submitted, the student cannot continue to answer, even if they have an extension on the due date. If you choose to use this setting, we advise you to warn your students against clicking**Submit**unless they are certain they want to forfeit the ability to increase their score.**After Due Date**: Reveal solutions to a given student when the due date passes for that student.**After Extended Due Date:**This option takes into account that some students may have later due dates than others because of extensions, or that late submissions may be allowed. Even if the due date has passed for a particular student, they cannot view solutions until the extended due date or late submission deadline has passed for all students.

**Unit 3** Scarcity, work, and choice

Themes and capstone units

How individuals do the best they can, and how they resolve the trade-off between earnings and free time

- Decision making under scarcity is a common problem because we usually have limited means available to meet our objectives.
- Economists model these situations, first by defining all of the feasible actions, then evaluating which of these actions is best, given the objectives.
- Opportunity costs describe the unavoidable trade-offs in the presence of scarcity: satisfying one objective more means satisfying other objectives less.
- A model of decision making under scarcity can be applied to the question of how much time to spend working, when facing a trade-off between more free time and more income.
- This model also helps to explain differences in the hours that people work in different countries, and the changes in our hours of work throughout history.

Imagine that you are working in New York, in a job that is paying you $15 an hour for a 40-hour working week, which gives you earnings of $600 per week. There are 168 hours in a week, so after 40 hours of work, you are left with 128 hours of free time for all your non-work activities, including leisure and sleep.

Suppose, by some happy stroke of luck, you are offered a job at a much higher wage—six times higher. Your new hourly wage is $90. Not only that, your prospective employer lets you choose how many hours you work each week.

Will you carry on working 40 hours per week? If you do, your weekly pay will be six times higher than before: $3,600. Or will you decide that you are satisfied with the goods you can buy with your weekly earnings of $600? You can now earn this by cutting your weekly hours to just 6 hours and 40 minutes (a six-day weekend!), and enjoy about 26% more free time than before. Or would you use this higher hourly wage rate to raise both your weekly earnings and your free time by some intermediate amount?

The idea of suddenly receiving a six-fold increase in your hourly wage and being able to choose your own hours of work might not seem very realistic. But we know from Unit 2 that technological progress since the Industrial Revolution has been accompanied by a dramatic rise in wages. In fact, the average real hourly earnings of American workers did increase more than six-fold during the twentieth century. And while employees ordinarily cannot just tell their employer how many hours they want to work, over long time periods the typical hours that we work do change. In part, this is a response to how much we prefer to work. As individuals, we can choose part-time work, although this may restrict our job options. Political parties also respond to the preferences of voters, so changes in typical working hours have occurred in many countries as a result of legislation that imposes maximum working hours.

So have people used economic progress as a way to consume more goods, enjoy more free time, or both? The answer is both, but in different proportions in different countries. While hourly earnings increased by more than six-fold for twentieth century Americans, their average annual work time fell by a little more than one-third. So people at the end of this century enjoyed a four-fold increase in annual earnings with which they could buy goods and services, but a much smaller increase of slightly less than one-fifth in their free time. (The percentage increase in free time would be higher if you did not count time spent asleep as free time, but it is still small relative to the increase in earnings.) How does this compare with the choice you made when our hypothetical employer offered you a six-fold increase in your wage?

Figure 3.1 shows trends in income and working hours since 1870 in three countries.

As in Unit 1, income is measured as per-capita GDP in US dollars. This is not the same as average earnings, but gives us a useful indication of average income for the purposes of comparison across countries and through time. In the late nineteenth and early twentieth century, average income approximately trebled, and hours of work fell substantially. During the rest of the twentieth century, income per head rose four-fold.

Hours of work continued to fall in the Netherlands and France (albeit more slowly) but levelled off in the US, where there has been little change since 1960.

While many countries have experienced similar trends, there are still differences in outcomes. Figure 3.2 illustrates the wide disparities in free time and income between countries in 2013. Here we have calculated free time by subtracting average annual working hours from the number of hours in a year. You can see that the higher-income countries seem to have lower working hours and more free time, but there are also some striking differences between them. For example, the Netherlands and the US have similar levels of income, but Dutch workers have much more free time. And the US and Turkey have similar amounts of free time but a large difference in income.

In many countries there has been a huge increase in living standards since 1870. But in some places people have carried on working just as hard as before but consumed more, while in other countries people now have much more free time. Why has this happened? We will provide some answers to this question by studying a basic problem of economics—scarcity—and how we make choices when we cannot have all of everything that we want, such as goods and free time.

Study the model of decision making that we use carefully! It will be used repeatedly throughout the course, because it provides insight into a wide range of economic problems.

**Question 3.1** Choose the correct answer(s)

Currently you work for 40 hours per week at the wage rate of £20 an hour. Your free hours are defined as the number of hours not spent in work per week, which in this case is 24 hours × 7 days − 40 hours = 128 hours per week. Suppose now that your wage rate has increased by 25%. If you are happy to keep your total weekly income constant, then:

- Your total number of working hours per week will fall by 25%.
- Your total number of working hours per week will be 30 hours.
- Your total number of free hours per week will increase by 25%.
- Your total number of free hours per week will increase by 6.25%.

- The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours. This represents a change of (32 – 40)/40 = -20%.
- The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours.
- The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours. Then your free time is now 24 hours per day × 7 days per week – 32 = 136 hours per week, an increase of (136 – 128)/128 = 6.25% ? 25%.
- The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours. Then your free time is now 24 × 7 – 32 = 136 hours per week, an increase of (136 – 128)/128 = 6.25%.

**Question 3.2** Choose the correct answer(s)

Look again at Figure 3.1, which depicts the annual number of hours worked against GDP per capita in the US, France and the Netherlands, between 1870 and 2000. Which of the following is true?

- An increase in GDP per capita causes a reduction in the number of hours worked.
- The GDP per capita in the Netherlands is lower than that in the US because Dutch people work fewer hours.
- Between 1870 and 2000, French people have managed to increase their GDP per capita more than ten-fold while more than halving the number of hours worked.
- On the basis of the evidence in the graph, one day French people will be able to produce a GDP per capita of over $30,000 with less than 1,000 hours of work.

- The negative relationship between the number of hours worked and GDP per capita does not necessarily imply that one causes the other.
- The lower GDP per capita in the Netherlands may be due to a number of factors, including the possibility that Dutch people may prefer less income but more leisure time for cultural or other reasons.
- The GDP per capita of France increased from roughly to $2,000 to $20,000 (ten-fold) while annual hours worked fell from over 3,000 to under 1,500.
- That would be nice. However past performance does not necessarily mean that the trend will continue in the future.

## 3.1 Labour and production

In Unit 2 we saw that labour can be thought of as an input in the production of goods and services. Labour is work; for example the welding, assembling, and testing required to make a car. Work activity is often difficult to measure, which is an important point in later units because employers find it difficult to determine the exact amount of work that their employees are doing. We also cannot measure the effort required by different activities in a comparable way (for example, baking a cake versus building a car), so economists often measure labour simply as the number of hours worked by individuals engaged in production, and assume that as the number of hours worked increases, the amount of goods produced also increases.

As a student, you make a choice every day: how many hours to spend studying. There may be many factors influencing your choice: how much you enjoy your work, how difficult you find it, how much work your friends do, and so on. Perhaps part of the motivation to devote time to studying comes from your belief that the more time you spend studying, the higher the grade you will be able to obtain at the end of the course. In this unit, we will construct a simple model of a student’s choice of how many hours to work, based on the assumption that the more time spent working, the better the final grade will be.

We assume a positive relationship between hours worked and final grade, but is there any evidence to back this up? A group of educational psychologists looked at the study behaviour of 84 students at Florida State University to identify the factors that affected their performance.^{1}

At first sight there seems to be only a weak relationship between the average number of hours per week the students spent studying and their Grade Point Average (GPA) at the end of the semester. This is in Figure 3.3.

The 84 students have been split into two groups according to their hours of study. The average GPA for those with high study time is 3.43—only just above the GPA of those with low study time.

Looking more closely, we discover this study is an interesting illustration of why we should be careful when we make *ceteris paribus* assumptions (remember from Unit 2 that this means ‘holding other things constant’). Within each group of 42 students there are many potentially important differences. The conditions in which they study would be an obvious difference to consider: an hour working in a busy, noisy room may not be as useful as an hour spent in the library.

In Figure 3.4, we see that students studying in poor environments are more likely to study longer hours. Of these 42 students, 31 of them have high study time, compared with only 11 of the students with good environments. Perhaps they are distracted by other people around them, so it takes them longer to complete their assignments than students who work in the library.

Now look at the average GPAs in the top row: if the environment is good, students who study longer do better—and you can see in the bottom row that high study time pays off for those who work in poor environments too. This relationship was not as clear when we didn’t consider the effect of the study environment.

So, after taking into account environment and other relevant factors (including the students’ past GPAs, and the hours they spent in paid work or partying), the psychologists estimated that an additional hour of study time per week raised a student’s GPA at the end of the semester by 0.24 points on average. If we take two students who are the same in all respects except for study time, we predict that the one who studies for longer will have a GPA that is 0.24 points higher for each extra hour: study time raises GPA by 0.24 per hour, *ceteris paribus*.

Exercise 3.1Ceteris paribusassumptionsYou have been asked to conduct a research study at your university, just like the one at Florida State University.

- In addition to study environment, which factors do you think should ideally be held constant in a model of the relationship between study hours and final grade?
- What information about the students would you want to collect beyond GPA, hours of study, and study environment?

Now imagine a student, whom we will call Alexei. He can vary the number of hours he spends studying. We will assume that, as in the Florida study, the hours he spends studying over the semester will increase the percentage grade that he will receive at the end, *ceteris paribus*. This relationship between study time and final grade is represented in the table in Figure 3.5. In this model, study time refers to all of the time that Alexei spends learning, whether in class or individually, measured per day (not per week, as for the Florida students). The table shows how his grade will vary if he changes his study hours, if all other factors—his social life, for example—are held constant.

- production function
- A graphical or mathematical expression describing the amount of output that can be produced by any given amount or combination of input(s). The function describes differing technologies capable of producing the same thing.

This is Alexei’s **production function**: it translates the number of hours per day spent studying (his input of labour) into a percentage grade (his output). In reality, the final grade might also be affected by unpredictable events (in everyday life, we normally lump the effect of these things together and call it ‘luck’). You can think of the production function as telling us what Alexei will get under normal conditions (if he is neither lucky nor unlucky).

If we plot this relationship on a graph, we get the curve in Figure 3.5. Alexei can achieve a higher grade by studying more, so the curve slopes upward. At 15 hours of work per day he gets the highest grade he is capable of, which is 90%. Any time spent studying beyond that does not affect his exam result (he will be so tired that studying more each day will not achieve anything), and the curve becomes flat.

- average product
- Total output divided by a particular input, for example per worker (divided by the number of workers) or per worker per hour (total output divided by the total number of hours of labour put in).

We can calculate Alexei’s average product of labour, as we did for the farmers in Unit 2. If he works for 4 hours per day, he achieves a grade of 50. The **average product**—the average number of percentage points per hour of study—is 50 / 4 = 12.5. In Figure 3.5 it is the slope of a ray from the origin to the curve at 4 hours per day:

- marginal product
- The additional amount of output that is produced if a particular input was increased by one unit, while holding all other inputs constant.

Alexei’s **marginal product** is the increase in his grade from increasing study time by one hour. Follow the steps in Figure 3.5 to see how to calculate the marginal product, and compare it with the average product.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

How does the amount of time spent studying affect Alexei’s grade?

Slideline showing how time spent studying affects Alexei’s grade

Figure 3.5 How does the amount of time spent studying affect Alexei’s grade?

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

Alexei’s production function

The curve is Alexei’s production function. It shows how an input of study hours produces an output, the final grade.

Figure 3.5a The curve is Alexei’s production function. It shows how an input of study hours produces an output, the final grade.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

Four hours of study per day

If Alexei studies for four hours his grade will be 50.

Figure 3.5b Four hours of study per day: If Alexei studies for four hours his grade will be 50.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

Ten hours of study per day

… and if he studies for 10 hours he will achieve a grade of 81.

Figure 3.5c Ten hours of study per day … and if he studies for 10 hours he will achieve a grade of 81.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

Alexei’s maximum grade

At 15 hours of study per day Alexei achieves his maximum possible grade, 90. After that, further hours will make no difference to his result: the curve is flat.

Figure 3.5d Alexei’s maximum grade: At 15 hours of study per day Alexei achieves his maximum possible grade, 90. After that, further hours will make no difference to his result: the curve is flat.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

Increasing study time from 4 to 5 hours

Increasing study time from 4 to 5 hours raises Alexei’s grade from 50 to 57. Therefore, at 4 hours of study, the marginal product of an additional hour is 7.

Figure 3.5e Increasing study time from 4 to 5 hours: Increasing study time from 4 to 5 hours raises Alexei’s grade from 50 to 57. Therefore, at 4 hours of study, the marginal product of an additional hour is 7.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

Increasing study time from 10 to 11 hours

Increasing study time from 10 to 11 hours raises Alexei’s grade from 81 to 84. At 10 hours of study, the marginal product of an additional hour is 3. As we move along the curve, the slope of the curve falls, so the marginal product of an extra hour falls. The marginal product is diminishing.

Figure 3.5f Increasing study time from 10 to 11 hours: Increasing study time from 10 to 11 hours raises Alexei’s grade from 81 to 84. At 10 hours of study, the marginal product of an additional hour is 3. As we move along the curve, the slope of the curve falls, so the marginal product of an extra hour falls. The marginal product is diminishing.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

The average product of an hour spent studying

When Alexei studies for four hours per day his average product is 50/4 = 12.5 percentage points, which is the slope of the ray from that point to the origin.

Figure 3.5g The average product of an hour spent studying: When Alexei studies for four hours per day his average product is 50/4 = 12.5 percentage points, which is the slope of the ray from that point to the origin.

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

The marginal product is lower than the average product

At 4 hours per day the average product is 12.5. At 10 hours per day it is lower (81/10 = 8.1). The average product falls as we move along the curve. At each point the marginal product (the slope of the curve) is lower than the average product (the slope of the ray).

Figure 3.5h The marginal product is lower than the average product: At 4 hours per day the average product is 12.5. At 10 hours per day it is lower (81/10 = 8.1). The average product falls as we move along the curve. At each point the marginal product (the slope of the curve) is lower than the average product (the slope of the ray).

Study hours | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 or more |

Grade | 0 | 20 | 33 | 42 | 50 | 57 | 63 | 69 | 73 | 78 | 81 | 84 | 86 | 88 | 89 | 90 |

The marginal product is the slope of the tangent

The marginal product at four hours of study is approximately 7, which is the increase in the grade from one more hour of study. More precisely, the marginal product is the slope of the tangent at that point, which is slightly higher than 7.

Figure 3.5-i The marginal product is the slope of the tangent: The marginal product at four hours of study is approximately 7, which is the increase in the grade from one more hour of study. More precisely, the marginal product is the slope of the tangent at that point, which is slightly higher than 7.

At each point on the production function, the marginal product is the increase in the grade from studying one more hour. The marginal product corresponds to the slope of the production function.

- diminishing returns
- A situation in which the use of an additional unit of a factor of production results in a smaller increase in output than the previous increase.
*Also known as: diminishing marginal returns in production*

Alexei’s production function in Figure 3.5 gets flatter the more hours he studies, so the marginal product of an additional hour falls as we move along the curve. The marginal product is **diminishing**. The model captures the idea that an extra hour of study helps a lot if you are not studying much, but if you are already studying a lot, then studying even more does not help very much.

- concave function
- A function of two variables for which the line segment between any two points on the function lies entirely below the curve representing the function (the function is convex when the line segment lies above the function).

In Figure 3.5, output increases as the input increases, but the marginal product falls—the function becomes gradually flatter. A production function with this shape is described as **concave**.

If we compare the marginal and average products at any point on Alexei’s production function, we find that the marginal product is below the average product. For example, when he works for four hours his average product is 50/4 = 12.5 points per hour, but an extra hour’s work raises his grade from 50 to 57, so the marginal product is 7. This happens because the marginal product is diminishing: each hour is less productive than the ones that came before. And it implies that the average product is also diminishing: each additional hour of study per day lowers the average product of all his study time, taken as a whole.

This is another example of the diminishing average product of labour that we saw in Unit 2. In that case, the average product of labour in food production (the food produced per worker) fell as more workers cultivated a fixed area of land.

Lastly, notice that if Alexei was already studying for 15 hours a day, the marginal product of an additional hour would be zero. Studying more would not improve his grade. As you might know from experience, a lack of either sleep or time to relax could even lower Alexei’s grade if he worked more than 15 hours a day. If this were the case, then his production function would start to slope downward, and Alexei’s marginal product would become negative.

- tangency
- When two curves share one point in common but do not cross. The tangent to a curve at a given point is a straight line that touches the curve at that point but does not cross it.

Marginal change is an important and common concept in economics. You will often see it marked as a slope on a diagram. With a production function like the one in Figure 3.5, the slope changes continuously as we move along the curve. We have said that when Alexei studies for 4 hours a day the marginal product is 7, the increase in the grade from one more hour of study. Because the slope of the curve changes between 4 and 5 hours on the horizontal axis, this is only an approximation to the actual marginal product. More precisely, the marginal product is the rate at which the grade increases, per hour of additional study. In Figure 3.5 the true marginal product is the slope of the **tangent** to the curve at 4 hours. In this unit, we will use approximations so that we can work in whole numbers, but you may notice that sometimes these numbers are not quite the same as the slopes.

Exercise 3.2Production functions

- Draw a graph to show a production function that, unlike Alexei’s, becomes steeper as the input increases.
- Can you think of an example of a production process that might have this shape? Why would the slope get steeper?
- What can you say about the marginal and average products in this case?

## Marginal product

The marginal product is the rate of change of the grade at 4 hours of study. Suppose Alexei has been studying for 4 hours a day, and studies for 1 minute longer each day (a total of 4.016667 hours). Then, according to the graph, his grade will rise by a very small amount—about 0.124. A more precise estimate of the marginal product (the rate of change) would be:

If we looked at smaller changes in study time even further (the rise in grade for each additional second of study per day, for example) we would get closer to the true marginal product, which is the slope of the tangent to the curve at 4 hours of study.

**Question 3.3** Choose the correct answer(s)

Figure 3.5 shows Alexei’s production function, with the final grade (the output) related to the number of hours spent studying (the input).

Which of the following is true?

- The marginal product and average product are approximately the same for the initial hour.
- The marginal product and the average product are both constant beyond 15 hours.
- The horizontal production function beyond 15 hours means that studying for more than 15 hours is detrimental to Alexei’s performance.
- The marginal product and the average product at 20 hours are both 4.5.

- Because there are no previous hours to consider, the average product for the initial hour is just the improvement produced by a single hour, which in turn approximates to the marginal product from 0 to 1 hours (the precise marginal product changes over this interval, reflected in the decreasing slope of the production function).
- The marginal product is constant beyond 15 hours, but the average product continues to diminish. This is because the marginal product (zero) is less than the average product, which remains positive but is decreasing (more hours with no additional improvement reduces the average).
- If studying for more than 15 hours had a negative effect on Alexei’s grade, then the marginal product would be negative, implying a downward-sloping curve beyond 15 hours.
- The average product at 20 hours is 90 grade points/20 hours = 4.5 points per hour. The marginal product, however, is zero – as indicated by the production function being flat beyond 15 hours.

## 3.2 Preferences

- preferences
- A description of the benefit or cost we associate with each possible outcome.

If Alexei has the production function shown in Figure 3.5, how many hours per day will he choose to study? The decision depends on his **preferences**—the things that he cares about. If he cared only about grades, he should study for 15 hours a day. But, like other people, Alexei also cares about his free time—he likes to sleep, go out or watch TV. So he faces a trade-off: how many percentage points is he willing to give up in order to spend time on things other than study?

We illustrate his preferences using Figure 3.6, with free time on the horizontal axis and final grade on the vertical axis. Free time is defined as all the time that he does not spend studying. Every point in the diagram represents a different combination of free time and final grade. Given his production function, not every combination that Alexei would want will be possible, but for the moment we will only consider the combinations that he would prefer.

We can assume:

- For a given grade, he prefers a combination with more free time to one with less free time. Therefore, even though both A and B in Figure 3.6 correspond to a grade of 84, Alexei prefers A because it gives him more free time.
- Similarly, if two combinations both have 20 hours of free time, he prefers the one with a higher grade.
- But compare points A and D in the table. Would Alexei prefer D (low grade, plenty of time) or A (higher grade, less time)? One way to find out would be to ask him.

- utility
- A numerical indicator of the value that one places on an outcome, such that higher valued outcomes will be chosen over lower valued ones when both are feasible.

Suppose he says he is indifferent between A and D, meaning he would feel equally satisfied with either outcome. We say that these two outcomes would give Alexei the same **utility**. And we know that he prefers A to B, so B provides lower utility than A or D.

A systematic way to graph Alexei’s preferences would be to start by looking for all of the combinations that give him the same utility as A and D. We could ask Alexei another question: ‘Imagine that you could have the combination at A (15 hours of free time, 84 points). How many points would you be willing to sacrifice for an extra hour of free time?’ Suppose that after due consideration, he answers ‘nine’. Then we know that he is indifferent between A and E (16 hours, 75 points). Then we could ask the same question about combination E, and so on until point D. Eventually we could draw up a table like the one in Figure 3.6. Alexei is indifferent between A and E, between E and F, and so on, which means he is indifferent between all of the combinations from A to D.

- indifference curve
- A curve of the points which indicate the combinations of goods that provide a given level of utility to the individual.

The combinations in the table are plotted in Figure 3.6, and joined together to form a downward-sloping curve, called an **indifference curve**, which joins together all of the combinations that provide equal utility or ‘satisfaction’.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Mapping Alexei’s preferences

Mapping Alexei’s preferences.

Figure 3.6 Mapping Alexei’s preferences.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Alexei prefers more free time to less free time

Combinations A and B both deliver a grade of 84, but Alexei will prefer A because it has more free time.

Figure 3.6a Combinations A and B both deliver a grade of 84, but Alexei will prefer A because it has more free time.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Alexei prefers a high grade to a low grade

At combinations C and D Alexei has 20 hours of free time per day, but he prefers D because it gives him a higher grade.

Figure 3.6b At combinations C and D Alexei has 20 hours of free time per day, but he prefers D because it gives him a higher grade.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Indifference

… but we don’t know whether Alexei prefers A or E, so we ask him: he says he is indifferent.

Figure 3.6c … but we don’t know whether Alexei prefers A or E, so we ask him: he says he is indifferent.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

More combinations giving the same utility

Alexei says that F is another combination that would give him the same utility as A and E.

Figure 3.6d Alexei says that F is another combination that would give him the same utility as A and E.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Constructing the indifference curve

By asking more questions, we discover that Alexei is indifferent between all of the combinations between A and D.

Figure 3.6e By asking more questions, we discover that Alexei is indifferent between all of the combinations between A and D.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Constructing the indifference curve

These points are joined together to form an indifference curve.

Figure 3.6f These points are joined together to form an indifference curve.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Other indifference curves

Indifference curves can be drawn through any point in the diagram, to show other points giving the same utility. We can construct other curves starting from B or C in the same way as before, by finding out which combinations give the same amount of utility.

Figure 3.6g Indifference curves can be drawn through any point in the diagram, to show other points giving the same utility. We can construct other curves starting from B or C in the same way as before, by finding out which combinations give the same amount of utility.

If you look at the three curves drawn in Figure 3.6, you can see that the one through A gives higher utility than the one through B. The curve through C gives the lowest utility of the three. To describe preferences we don’t need to know the exact utility of each option; we only need to know which combinations provide more or less utility than others.

- consumption good
- A good or service that satisfies the needs of consumers over a short period.

The curves we have drawn capture our typical assumptions about people’s preferences between two goods. In other models, these will often be **consumption goods** such as food or clothing, and we refer to the person as a consumer. In our model of a student’s preferences, the goods are ‘final grade’ and ‘free time’. Notice that:

*Indifference curves slope downward due to trade-offs*: If you are indifferent between two combinations, the combination that has more of one good must have less of the other good.*Higher indifference curves correspond to higher utility levels*: As we move up and to the right in the diagram, further away from the origin, we move to combinations with more of both goods.*Indifference curves are usually smooth*: Small changes in the amounts of goods don’t cause big jumps in utility.*Indifference curves do not cross*: Why? See Exercise 3.3.*As you move to the right along an indifference curve, it becomes flatter*.

- marginal rate of substitution (MRS)
- The trade-off that a person is willing to make between two goods. At any point, this is the slope of the indifference curve.
*See also: marginal rate of transformation.*

To understand the last property in the list, look at Alexei’s indifference curves, which are plotted again in Figure 3.7. If he is at A, with 15 hours of free time and a grade of 84, he would be willing to sacrifice 9 percentage points for an extra hour of free time, taking him to E (remember that he is indifferent between A and E). We say that his **marginal rate of substitution (MRS)** between grade points and free time at A is nine; it is the reduction in his grade that would keep Alexei’s utility constant following a one-hour increase of free time.

We have drawn the indifference curves as becoming gradually flatter because it seems reasonable to assume that the more free time and the lower the grade he has, the less willing he will be to sacrifice further percentage points in return for free time, so his MRS will be lower. In Figure 3.7 we have calculated the MRS at each combination along the indifference curve. You can see that, when Alexei has more free time and a lower grade, the MRS—the number of percentage points he would give up to get an extra hour of free time—gradually falls.

A | E | F | G | H | D | |
---|---|---|---|---|---|---|

Hours of free time | 15 | 16 | 17 | 18 | 19 | 20 |

Final grade | 84 | 75 | 67 | 60 | 54 | 50 |

Marginal rate of substitution between grade and free time | 9 | 8 | 7 | 6 | 4 |

The marginal rate of substitution

The marginal rate of substitution.

Figure 3.7 The marginal rate of substitution.

Alexei’s indifference curves

The diagram shows three indifference curves for Alexei. The curve furthest to the left offers the lowest satisfaction.

Figure 3.7a The diagram shows three indifference curves for Alexei. The curve furthest to the left offers the lowest satisfaction.

Point A

At A, he has 15 hours of free time and his grade is 84.

Figure 3.7b At A, he has 15 hours of free time and his grade is 84.

Alexei is indifferent between A and E

He would be willing to move from A to E, giving up 9 percentage points for an extra hour of free time. His marginal rate of substitution is 9. The indifference curve is steep at A.

Figure 3.7c He would be willing to move from A to E, giving up 9 percentage points for an extra hour of free time. His marginal rate of substitution is 9. The indifference curve is steep at A.

Alexei is indifferent between H and D

At H he is only willing to give up 4 points for an extra hour of free time. His MRS is 4. As we move down the indifference curve, the MRS diminishes, because points become scarce relative to free time. The indifference curve becomes flatter.

Figure 3.7d At H he is only willing to give up 4 points for an extra hour of free time. His MRS is 4. As we move down the indifference curve, the MRS diminishes, because points become scarce relative to free time. The indifference curve becomes flatter.

All combinations with 15 hours of free time

Look at the combinations with 15 hours of free time. On the lowest curve the grade is low, and the MRS is small. Alexei would be willing to give up only a few points for an hour of free time. As we move up the vertical line the indifference curves are steeper: the MRS increases.

Figure 3.7e Look at the combinations with 15 hours of free time. On the lowest curve the grade is low, and the MRS is small. Alexei would be willing to give up only a few points for an hour of free time. As we move up the vertical line the indifference curves are steeper: the MRS increases.

All combinations with a grade of 54

Now look at all the combinations with a grade of 54. On the curve furthest to the left, free time is scarce, and the MRS is high. As we move to the right along the red line he is less willing to give up points for free time. The MRS decreases–the indifference curves get flatter.

Figure 3.7f Now look at all the combinations with a grade of 54. On the curve furthest to the left, free time is scarce, and the MRS is high. As we move to the right along the red line he is less willing to give up points for free time. The MRS decreases–the indifference curves get flatter.

The MRS is just the slope of the indifference curve, and it falls as we move to the right along the curve. If you think about moving from one point to another in Figure 3.7, you can see that the indifference curves get flatter if you increase the amount of free time, and steeper if you increase the grade. When free time is scarce relative to grade points, Alexei is less willing to sacrifice an hour for a higher grade: his MRS is high and his indifference curve is steep.

As the analysis in Figure 3.7 shows, if you move up the vertical line through 15 hours, the indifference curves get steeper: the MRS increases. For a given amount of free time, Alexei is willing to give up more grade points for an additional hour when he has a lot of points compared to when he has few (for example, if he was in danger of failing the course). By the time you reach A, where his grade is 84, the MRS is high; grade points are so plentiful here that he is willing to give up 9 percentage points for an extra hour of free time.

You can see the same effect if you fix the grade and vary the amount of free time. If you move to the right along the horizontal line for a grade of 54, the MRS becomes lower at each indifference curve. As free time becomes more plentiful, Alexei becomes less and less willing to give up grade points for more time.

Exercise 3.3Why indifference curves never crossIn the diagram below, IC

_{1}is an indifference curve joining all the combinations that give the same level of utility as A. Combination B is not on IC_{1}.

- Does combination B give higher or lower utility than combination A? How do you know?
- Draw a sketch of the diagram, and add another indifference curve, IC
_{2}, that goes through B and crosses IC_{1}. Label the point at which they cross as C.- Combinations B and C are both on IC
_{2}. What does that imply about their levels of utility?- Combinations C and A are both on IC
_{1}. What does that imply about their levels of utility?- According to your answers to (3) and (4), how do the levels of utility at combinations A and B compare?
- Now compare your answers to (1) and (5), and explain how you know that indifference curves can never cross.

Exercise 3.4Your marginal rate of substitutionImagine that you are offered a job at the end of your university course with a salary per hour (after taxes) of £12.50. Your future employer then says that you will work for 40 hours per week leaving you with 128 hours of free time per week. You tell a friend: ‘at that wage, 40 hours is exactly what I would like.’

- Draw a diagram with free time on the horizontal axis and weekly pay on the vertical axis, and plot the combination of hours and the wage corresponding to your job offer, calling it A. Assume you need about 10 hours a day for sleeping and eating, so you may want to draw the horizontal axis with 70 hours at the origin.
- Now draw an indifference curve so that A represents the hours you would have chosen yourself.
- Now imagine you were offered another job requiring 45 hours of work per week. Use the indifference curve you have drawn to estimate the level of weekly pay that would make you indifferent between this and the original offer.
- Do the same for another job requiring 35 hours of work per week. What level of weekly pay would make you indifferent between this and the original offer?
- Use your diagram to estimate your marginal rate of substitution between pay and free time at A.

**Question 3.4** Choose the correct answer(s)

Figure 3.6

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