# SAINT MARYS UNIVERSITY Department of Economics Econ 4400.1 Assignment # 3

SAINT MARYS UNIVERSITY

Department of Economics

Econ 4400.1

Assignment # 3

1. A perfectly competitive firm has the following cost function:

C = 1/3Q3  10Q2 +100Q  2KQ + K2

a. Determine the firms long-run cost function.

b. Determine the firms cost function that applies to its optimal plant.

c. What output the firm will produce in the long-run and what price it will charge for this output?

d. Calculate the firms profit at the output level you found above.

e. What is the equation for the firms short-run inverse supply function?

f. Compute the changes that will take place in your answers to parts a-e above if a carbon tax of \$5 per unit is imposed on the firms production.

2. Consider a firm that has the following production function: Q = 10K0.5L0.5. Assume prices of labour and capital to be \$10 and \$40, respectively and that 4 unit of capital are used. Market demand is: QD,M = 10,000  500P.

a. Assume the firm is operating in a perfectly competitive market where there are 100 identical firms. Calculate the firms short-run output, price and profit.

b. Now assume a single firm gains control of the entire market. Assuming all other conditions remain the same, calculate the monopolists short-run output, price and profit.

c. Calculate the deadweight loss that results due to monopolization of this industry.

3. A monopoly sells a product to two groups of consumers in different parts of the country. Group 1s elasticity of demand is -3, while group 2s is -5.

a. If the monopolist charges a price of \$10 to group 1s consumers, how much should it charge to group 2?

b. Are the above prices profit maximizing if marginal cost of production is \$40?

4. Assume a monopolist produces its output in two different plants, where the production processes in the two plants are characterized by two different cost curves, reflecting the fact that one plant is more efficient than the other. In general, why does not the monopolist simply always produce all of its output in the plant processing the lower cost curve? Illustrate your response with graphs.

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