Managerial Economics

Important: Clearly show your calculation steps where applicable or no credit

Please staple your homework;

Problem 1(Derived Demand Curve for E-books) (20 points):

In 2014, an average American book reader Jackie spent about 20% of book budget on e-books (X), and 80% on print books (Y);

Assume his annual book budget was $50, the average price of e-books was $10, and the average price of print books was $20. (Px = $10, Py = $20, I = $50)

1) Define a utility function that represents his preference for book consumption. Use Lagrangian method to solve for the optimal consumption of e-books and print books that makes Jackie most satisfied; Solve the first order conditions and Show your work. (4 points)

2) Derive a demand function for e-books in terms of Px, Py and budget I. (4 points)

3) Graph the budget line and indifference curves. Mark the intercepts of the budget line and the slope, and mark the optimal solutions. (2 points)

4) Suppose the average price of e-books increased to PxA = $12, and the average price of print books stayed same Py = $20. How many e-books and print books would Jackie have purchased in 2014 in order to maximize his satisfaction? (3 points)

5) Plot the new budget line and show the new optimal solutions in your graph in part 5). Compare the new solution with the previous consumption bundle in part 2), did consumer’s utility increase or decrease when e-books price increased from $10 to $12? (3 points)

6) Graph the derived demand curve of e-books for Jackie (X-axis: X Quantity of E-Books, Y-axis: Price of e-books Px). (4 points)

Problem 2 (Change in Consumer Surplus due to E-books Price Increase) (12 points):

1) Based on the derived demand function for e-books, calculate change in consumer surplus (?CS) for Jackie when average price of e-books increases from $10 to $12. (5 points) (Hint: refer to example 5.1 in Textbook p143)

2) Show the area of change in consumer surplus in your graph in Problem 1 part 6). (2 points)

3) Assume that there are 220 million book readers in the U.S, in 2014, what is the total loss of consumer surplus due to increase in e-books prices? (5 points)

(Note: Through this exercise, we have just estimated the loss to consumers when e-book prices are fixed at a higher level than its competitive price. Apple has recently agreed to compensate consumers $450 million for e-book price fixing case. For more information, see Optional Reading #5 _ Apple E-Books Price Fixing, WSJ, 6/30/2015; More background information on Apple e-books price fixing case can be found at

https://en.wikipedia.org/wiki/United_States_v._Apple_Inc )

Problem 3. (Short-run production) (10 points):

Given the following total production output at various labor input level, fill out the corresponding Average Product of Labor and Marginal Product of Labor, where

AP = q/L ; MP = ?q / ?L

(Note that in the short run, capital K is held constant at 10 units)

Labor (L) Capital (K) Total Production (q) Average Product (AP) Marginal Product (MP)

0 10 0

1 10 10

2 10 30

3 10 60

4 10 80

5 10 95

6 10 108

7 10 112

8 10 112

9 10 108

10 10 100

1) Graph the total production curve, AP curve and MP curve, and identify the three stages of production; (6 points)

2) Identify the Labor input level where MP reaches its max and AP reaches its max. Mark in the graph. (4 points)

Problem 4. (Short-run production) (10 points):

Given the following short-run production function

q = 21L + 9L2 – L3 where L is labor hours.

1) Solve for Labor (L) input level where Marginal Product (MP) reaches maximum;

2) Solve for Labor (L) input level where Average Product (AP) reaches maximum;

3) Solve for Labor (L) input level where total production q reaches maximum;

Problem 5. (Long-run production) (8 points):

The data below show the combinations of labor and capital that produce the same level of output for a U.S. firm producing electronics.

Labor (L) Capital (K) Output (q)

2 18 6

3 12 6

4 8 6

6 6 6

7 5 6

9 4 6

12 3 6

13 2.75 6

18 2 6

1) Graph the isoquant for q = 6;

2) Calculate the MRTSLK at (L=2, K=18), (L=3, K=12), (L=6, K=6), and (L=12, K=3)

Problem 6 (Return to Scale) (12 points):

Does the following production functions exhibit constant, increasing, or decreasing returns to scale? Show your work.

1) q = 3L + 2K

2) q = (3L + 2K)1/2

3) q = min (3L, 2K)

4) q = 3LK2

5) q = 100 (K0.8L0.2)

6) q = 100 (K0.9L0.2)

Problem 7 (Calculate Consumer Surplus with a Linear Demand Function) (10 points):

Given the following linear demand curve for processed pork in Canada you have solved in Homework 1 Problem 3:

QD = 295 – 20P

where P is the price of processed pork ($/kg), and QD is quantity demanded in millions of kg.

1) Calculate consumer surplus at P = $5/kg; Graph the demand curve and show the area of consumer surplus. (4 points)

2) Calculate consumer surplus at P = $4/kg; Graph the demand curve and show the area of consumer surplus. (4 points)

3) What is the change in consumer surplus when price of pork decreases from $5/kg to $4/kg? (2 points)