# Calculating marginal and average products, and Lerner Index

1. The following table shows data for a simple production function.

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

Column 1 numbers = Capital ; Column 2 numbers = Labor; Column 3 numbers= Total Product

10 0 0

10 1 5

10 2 15

10 3 30

10 4 50

10 5 75

10 6 85

10 7 90

10 8 92

10 9 92

10 10 90

a. From the information in the table, calculate marginal and average products.

b. Graph the three functions on separate graphs (Total production, Marginal Products and Average Products).

c. For what range of output does this function have diminishing marginal returns?

d. At what output is average product maximized?

2. Suppose the demand curve for a monopolist is QD= 500 - P, and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit.

a. Find the monopolist's profit-maximizing output and price.

b. Calculate the monopolist's profit.

c. What is the Lerner Index for this industry?

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#### Solution Preview

1.

a) See the attached Excel file.

b) See the attached Excel file.

c) The range L > 5

d) When L = 5 and AP = 25

2.

a) Profit is maximized when ...

#### Solution Summary

This solution gives detailed calculations showing how to:

1. Calculate marginal and average product, graph the resulting functions, and use the data to determine the maximum average product.

2. Calculate a monopolist's profit-maximizing price, output and profit, and use the result to determine the Lerner Index for the industry.

Microeconomic Multiple Choice

1.Consider the following entry game. Here, firm B is an existing firm in the market, and firm A is a potential entrant. Firm A must decide whether to enter the market (play "enter") or stay out of the market (play "not enter"). If firm A decides to enter the market, firm B must decide whether to engage in a price war (play "hard"), or not (play "soft"). By playing "hard", firm B ensures that firm A makes a loss of $1 million, but firm B only makes $1 million in profits. On the other hand, if firm B plays "soft", the new entrant takes half of the market, and each firm earns profits of $5 million. If firm A stays out, it earns zero while firm B earns $10 million. Which of the following are Nash equilibrium strategies?

a) (enter, hard) and (not enter, hard)

b) (enter, soft) and (not enter, soft)

c) (not enter, hard) and (enter, soft)

d) (enter, hard) and (not enter, soft)

2.Suppose P = 20 - 2Q is the market demand function for a local monopoly. The marginal cost is 2Q. If fixed costs are zero and the firm engages in two-part pricing, the most profits the firm will earn is:

a) $5.

b) $10.

c) $25.

d) $50.

3. play 2

t1 t2 t3

play 1 S1 10,0 5,1 4,-200

S2 10,100 5,0 0,-100

Which of the following pair of strategies constitute a Nash equilibrium of the game?

a) S1, t1

b) S1, t2

c) S2, t1

d) both b and c

4.Suppose that the duopolists competing in Cournot fashion agree to produce the collusive output. Given that firm one commits to this collusive output, it pays firm two to

a) cheat by producing more output.

b) cheat by producing less output.

c) cheat by raising prices.

d) none of the above

5.The production function for a competitive firm is Q = K.5L.5. The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at one unit. The maximum profits are

a. 5.

b. 10.

c. 15.

d. none of the above.

6. When there are economies of scope between products, selling off an unprofitable subsidiary

a) could lead to a major reduction in costs.

b) could lead to only a minor reduction in costs.

c) could lead to only a minor reduction in sales.

d) could lead to a major reduction in sales.

7. The industry elasticity of demand for gadgets is -2, while the elasticity of demand for an individual gadget manufacturer's product is -2. Based on the Rothschild approach to measuring market power, we conclude that

a) there is little monopoly power in this industry.

b) there is significant monopoly power in this industry.

c) the Herfindahl index for this industry is -2.

d) the Herfindahl index for this industry is 2.

8.A student in a managerial economics class calculated the four-firm concentration ratio and HHI for industries A and B. What is the proper conclusion she can draw from the following findings?

Industry A Industry B

4-Firm CR 0.9 1

HHI 3200 2500

a) Industry B is a monopoly.

b) The market power of firms in industry A is greater than that in industry B.

c) C4 is higher for Industry A while the HHI is higher for Industry B. This inconsistency must be due to a calculation error.

d) Neither industry is perfectly competitive.

9.If the profit-maximizing markup factor in a 3-firm Cournot oligopoly is -2, what is the corresponding market elasticity of demand?

a) -1/2.

b) -2/3.

c) -1.0.

d) -2.0.

10.A local video store estimates their average customer's demand per year is Q = 7 - 2P, and knows the marginal cost of each rental is $0.5. How much should the store charge for an annual membership in order to extract all the consumer surplus via an optimal two-part pricing strategy?

a) $9.

b) $10.

c) $11.

d) $12.

11.Eric provides cheese (H) and milk (M) to the market with the following total cost function C(H, M) = 10 + 0.4 H2 + 0.2M2. The price of cheese and milk in the market are $2 and $5 respectively. Assume that the cheese and milk markets are perfectly competitive. What output of milk maximizes profits?

a) 1.25.

b) 12.5.

c) 15.

d) 20.

12.An unregulated industry has a Lerner index of zero. These numbers:

a) reveal that social welfare would be improved by regulating the firms.

b) are consistent with the industry being monopolistically competitive.

c) are consistent with the industry being perfectly competitive.

d) a. and b.