1. Given the following production function: q = 10KL
a) If w = 25, r = 75, and C = 1200, mathematically find the minimum cost combination of capital and labour to produce a given level of output.
b) Does the production function in part (a) show increasing returns to scale, decreasing returns to scale, or constant returns to scale? Explain.
c) Using isoquants and isocosts, graphically illustrate the effect of an increase in the wage rate (assume the firm is producing at the same level of output).
2. Given the following total cost function facing a perfectly competitive firm:
TC = 500 + 10q2
a) If price = 100, determine the level of output and profit earned by the firm in the short-run.
b) Based on your answer for part (a), should the firm continue to produce in the short-run? Why or why not?
c) Graphically illustrate a perfectly competitive firm earning a positive profit, zero profit, and incurring a loss in the short-run.
3. Given the following inverse demand and supply functions:
P = 40 - 2Q
P = 10 + 3Q
(a) Determine the equilibrium quantity and the equilibrium price.
(b) If the government imposes a $10/unit tax on the seller, determine the after tax equilibrium quantity and price. How much of the tax is paid by the seller and the buyer?
(c) If the government now imposes a $10/unit tax on the buyer instead, determine the after tax equilibrium quantity and price. How much of the tax is paid by the seller and buyer?
4. Given the following information for a monopolist:
P = 40 - 2Q
TC = 4Q + 4Q2
(a) Determine the profit-maximizing level of output and price charged by the monopolist.
(b) Determine the profit level.
(c) Graphically illustrate a monopolist earning a profit in the short-run.
5. To increase profits, a monopolist has decided to engage in third-degree price discrimination by separating its customers into two groups and charging different prices for each group.
a) What type of price discrimination is the firm planning to engage in? Graphically illustrate the effect on price and output for both groups of customers.
b) Given the following two demand functions and overall marginal cost, determine the output produced and price charged for each group:
P = 2000 - 5Q
P = 100 - Q
MC = 10
c) Compare the results from part (b) between the two groups.
6. Marge's Beauty Salon sells shampoo and conditioner. Marge has two types of customers. Their willingness-to-pay for shampoo and conditioner are given in the table below. If Marge bundles the shampoo and conditioner, could she increase revenue? Show your calculation.
|
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Shampoo
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Conditioner
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|
Type I
|
8
|
5
|
|
Type II
|
6
|
8
|
7. a) Assuming competitive factor markets, graphically illustrate and explain the difference between marginal revenue product for a competitive output market and a monopolistic output market.
b) Assuming competitive factor markets, graphically illustrate and discuss the effect of an increase in the wage rate in a competitive labour market.
Graphically derive the long run demand curve in a competitive factor market and explain the underlying theory.