# Problem set 2

Due by **11:59 PM** on Friday, January 26, 2018

**Submit this as a PDF on Learning Suite.** Show your work when possible. You can use whatever you want to make your drawings, including Adobe Illustrator, Excel, PowerPoint, Microsoft Paint, Desmos, or scanned pen and paper.

## 1

In 1991, the New York Times reported on a study using the headline “Study Finds Enrollment Is Up At Colleges Despite Recession.”William Celis III, “Study Finds Enrollment Is Up At Colleges Despite Recession,” December 28, 1991.

How would you rewrite this headline now that you understand the idea of opportunity cost? Why?

## 2

Recall Alexei’s production function with diminishing marginal product.

- 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?

## 3

By tradition if no longer by law, school uniforms are a requirement for a young person to attend secondary school in Kenya. However, uniforms are expensive and this cost constitutes a barrier to secondary school attendance for some students. A recently conducted social experiment in that country found that giving out school uniforms for free to some randomly selected students just finishing elementary school caused these selected students to have lower dropout rates, that is, more of them went on to secondary school, as compared to students who did not receive the free uniforms.David Evans, Michael Robert Kremer, and Mũthoni Ngatia, “The Impact of Distributing School Uniforms on Children’s Education in Kenya,”.

Economists explained this result by saying this experimental program had for these students “increased the opportunity cost of dropping out of school.” What did they mean by this?

## 4

The utility functions for three people, where \(w =\) waffles (measured in waffles per week) and \(b =\) bacon (measured in strips of bacon per week) are:

- R. Swanson: \(U_S = 5w + 3b\)
- J.Or G. or L. or T. or B.

Gergich: \(U_G = 0.2wb\) - L. Knope: \(U_K = \sqrt{wb}\)

- If they all consume 4 waffles and 10 strips of bacon, who is best off? Explain.
- If \(w =\) 4, what is the marginal utility of the 11th and 12th strip of bacon for each person?
- Which of these functions most closely corresponds to our notions about consumer behavior? Why?

## 5

Imagine that you are offered a job after you graduate with your MPA with a salary per hour (after taxes) of $30. Your future employer then says that you will work for 40 hours per week leaving you with 128 hours of free time per week.Since 24 × 7 = 168 and 168 − 40 = 128.

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.

## 6

- Describe a situation in which Alexei’s grade points and free time would not be scarce. Remember, scarcity depends on both his preferences and the production function.
- What could bring about a technological improvement in his production function and those of his fellow students?
- Draw a diagram to illustrate how this improvement would affect the feasible set of grades and study hours.
- Analyze what might happen to Alexei’s choice of study hours. What might your choice be? How are those choices determined?

## 7

Consider a mild-mannered (immortal) architect named Michael He’s so nice.

whose utility function for slices of Hawaiian pizza per week (\(p\)) and cups of frozen yogurt per week (\(y\)) and is \(U_M = \sqrt{py}\). For this function, \(MRS = \frac{y}{p}\).

- Graph Michael’s indifference curves for \(U_M =\) 10 and \(U_M =\) 5, labeling axes and curves. Put pizza (\(p\)) on the x-axis.
- If the price of pizza is $1 per slice and frozen yogurt is $2 per cup, what can you guess about Michael’s consumption?
- If Michael has a budget of $10 per week to spend on these two foods, and pizza costs $1 per slice and frozen yogurt costs $2 per cup, how much of each food will Michael consume? How many utils will Michael enjoy?