SAINT MARYS UNIVERSITY Department of Economics Econ 4400.1 Assignment # 3
SAINT MARYS UNIVERSITY
Department of Economics
Assignment # 3
1. A perfectly competitive firm has the following cost function:
C = 1/3Q3 10Q2 +100Q 2KQ + K2
a. Determine the firms long-run cost function.
b. Determine the firms 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 firms profit at the output level you found above.
e. What is the equation for the firms 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 firms 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 firms 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 monopolists 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 1s elasticity of demand is -3, while group 2s is -5.
a. If the monopolist charges a price of $10 to group 1s 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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