Note that you need to show your work to get credit. There are nine questions in total. Please make sure that your answers are neatly typed or written out.

  1. You are in process of preparing for your upcoming exam. The production process between hours spent studying (input) and your exam score can be mapped by the following empirical production process.
hours study exam score
0 0
1 30
2 46
3 55
4 62
5 67
6 71
7 75
8 77
9 81
10 83
11 85
12 87
13 89
14 90
15 90
16 90

Table 1.

  1. In a separate column, calculate the average product per hour you spend studying.

  2. In another column, calculate the marginal product per additional hour you spend studying.

  3. Plot the empirical production function as given by Figure 1, the average and marginal product per hour spent studying on a graph.

  4. What can you say about the relationship between the marginal and average product per hour spent studying. Why is the relationship as it is?

 

  1. The following figure plots the empirical production function as presented in Table 1, along with tangential lines at points A and B.
Figure 1.

Figure 1.

  1. Using Table 1 and Figure 1 estimate the slope of the tangential line running across point A.

  2. Estimate the slope of the tangential line of point B.

  3. Using you answers from part a and b, what can you say about the number of hours spent studying and diminishing marginal product of labor?

 

  1. A convex production function.

  1. Draw a graph to show a production function that, unlike Maya’s, becomes steeper as the input increases.

  2. Can you think of an example of a production process that might have this shape? Why would the slope get steeper?

  3. What can you say about the marginal and average products in this case?

 

  1. Based on the information given in Table 1 (the empirical production function), which of the following is true?

\(\underline{choice\;1}\) The marginal product is greater than the average product for the first hour.

\(\underline{choice\;2}\) The marginal product is zero but the average product keeps decreasing beyond the \(15^{th}\) hour.

\(\underline{choice\;3}\) Slope of the production function is never equal to zero.

\(\underline{choice\;4}\) The average cost can rise even if the marginal cost falls.

 

  1. Consider that you care about both your score and your leisure time. It is obvious from Table 1 that there is a trade-off between hours spent studying and time you have left for leisure. Say your preference set between exam score and leisure is as follows:
A’ B’ C’ D’ E’ F’ G’ H’ I’
Final Score 79.5 80 81 81.8 83 85.5 88.5 91.5 94.5
Free Time 20.0 18 16 15.0 14 13.0 12.0 11.0 10.0

Table 2.

Note that you are indifferent between any of these points – each point gives you the same level of happiness.

  1. Express your preference set in Figure 2 by using an indifference curve.

  2. Calculate the marginal rate of substitution when you move from preference A’ to B’ vs. when you move from H’ to I’.

 

  1. Consider your friend Alexis’s preference set in Table 3 below.
A E F G H D
Final Score 84 75 67 60 54 50
Free Time 15 16 17 18 19 20

Table 3.

Which of the following is true?

\(\underline{choice 1}\) Alexei prefers C to B because at C he has more free time.

\(\underline{choice 2}\) Alexei is indifferent between the grade of 84 with 15 hours of free time, and the grade of 50 with 20 hours of free time.

\(\underline{choice 3}\) Alexei prefers D to C, because at D he has the same grade and more free time.

\(\underline{choice 4}\) At G, Alexei is willing to give up 2 hours of free time for 10 extra grade points.

 

  1. You work in a resturant as a waiter and make $100 per day. You have been offered a ticket to go watch your favorite band play for $50. As a fan, you value watching them perform live at $200. Given this information, what can we say?

\(\underline{choice 1}\) The opportunity cost of watching the band play is $50.

\(\underline{choice 2}\) The economic cost of watching the band is $50.

\(\underline{choice 3}\) The economic rent of watching the band play is $50.

\(\underline{choice 4}\) You would have paid $200 for the ticket.

 

  1. The question of how many hours you decide to study depends on you production process (Table 1) and preferences (Table 2).

  1. Using Table 1 and Table 2, find your optimal studying time. hint: First, plot your score in Table 1 as hours of free time, then plot your preference score in Table 2 on the same graph. Look at the intersection point.

  2. Comment about the MRS (slope of the indifference curve) and MRT (slope of the production frontier) at the optimal point.

Figure 1.

Figure 1.

  1. This problem refers to the demand equation. Consider the following demand schedule.
price quantity
10 2
9 4
8 6
7 8
6 10
5 12
4 14
3 16
2 18
1 20

  1. Find the demand equation. Write down the equation specifically in the form \(Q=mP+C\), where \(Q\) is the quantity demanded, \(P\) is the price, \(m\) is the slope, and \(c\) is the y-intercept.

  2. Next, calculate the arc-price elasticity of demand between these two points on the demand curve: a) \(price=4\) and b) \(price=3\).

  3. Calculate the point elasticity of the demand when: a) \(price=3\) and b) \(price=8\).

  4. Given the magnitude of the point elasticity of the demand as calcuated in question c, comment on the variation of price elasticity of demand over a demand curve.