Principles of Microeconomics Problem Set #3 University of Alaska, Anchorage Lance Howe, Spring 2006

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1 Principles of Microeconomics Problem Set #3 University of Alaska, Anchorage Lance Howe, Spring 2006 Elasticity, Inputs, and the Firm in Perfect Competition Instructions: Answer each question completely. For this problem set you can choose to work with one other person. Turn in one problem set and put both names in the space above. I. Elasticity 1.) Suppose that the monthly demand for housing in Anchorage is Q D = P. a.) Using the formula for elasticity we have described in class, suppose that the initial price is $400 dollars, calculate the price elasticity of demand between a price of $500 and $400. Explain the meaning of your answer using the concept of elasticity. b.) Suppose that the prevailing price is $400. Would you recommend an increase in the price to $500, why or why not? Explain using the concept of elasticity. If not, describe the conditions under which you could make such a recommendation. c.) Calculate the total revenue first from the sale of houses at a price of $400 and then at a price of $500. Do you reach a different conclusion regarding the effect of the increase in price? d.) Suppose that when an average customers income increases rises from $18,000 to $22,000 per year, annual housing purchases increase from 5,500 units to 6,700 units. Calculate the income elasticity of demand. Is housing a normal good? Why or why not? Page 1 of 5

2 e.) If the monthly price of rental housing increased by 20% from $400 to $480, use the concept of cross-price elasticity to carefully explain the impact of this price change on the demand for townhouses (assuming that the price of other types of housing has remained relatively constant). f.) Under what condition would you unambiguously recommend a firm to increase their price? III. Optimal Choice of Inputs Jewel was recently was hired to manage Durable Jeans Inc.. The shop sells jeans for $50 each. The fixed cost of keeping the factory open is $200 per day. Jewel is trying to decide how many workers to employ at $50 per day. Here is some relevant data: Q Workers TPP a. The marginal physical product of the 4 th worker is what? b. The marginal revenue of product of the 2 nd worker is what? c. To minimize costs (and consequently to maximize profits), the store should employ how many workers? d. What is the profit maximizing level of output? Does it differ from your answer in part c? What is the amount of profit? e. Does the principle of diminishing returns to labor seem to apply in the above example? Explain how this concept is related to increasing marginal costs. Page 2 of 5

3 IV. Perfect Competition: Long Run and Short Run Suppose that a representative firm in the perfectly competitive grape juice industry is producing at a point where price per gallon is equal to $1.50, marginal cost is $1.50, average cost is $1.50 and quantity is 100 gallons per day. There are 10 such firms in the industry. a. Use the space provided to illustrate this equilibrium. In the graph at left draw the industry supply and demand curves, being sure to give values for industry price and quantity based on the given information. In the graph at right illustrate the cost curves (average cost, marginal cost and average variable cost) and marginal revenue for the typical juice firm. Also label price and quantity for the representative firm. b. Now suppose that a publicized study conclusively demonstrates that regular consumption of grape juice greatly reduces the risk of heart disease and also acts as a preventative agent against the common cold. Answer the following questions: i.) If most people would like to reduce the effects of the common cold as well as their risk of heart disease, verbally expain what this new study will do to the industry demand for juice? ii) In the graph at right, show how the equilibrium price in the industry might change in the short-run? If the price does change and you think the price increases label the new price $2 and the industry supply at If you think the price will decrease, then let the new price be $1 and the new quantity 500. Page 3 of 5

4 iii) On the graph at right indicate the cost curves and the new marginal revenue curve for the representative grape juice firm. If all firms are identical how many units does the representative firm now produce? Be sure to label everything, and make your answer consistent with the price you chose in part (ii). iv) In the short run, how does industry supply change? How does the firms quantity supplied change? If average cost is $1.75 at the profit maximizing level of output after this increase in demand what is the firms profit? Indicate this region in your graph for part (iii). c. In the long-run, however, we know that negative and positive economic profits cannot persist. i.) What will be the long-run response of grape juice producers to this permanent shift in demand? Explain how this change in the industry will affect equilibrium price and equilibrium quantity produced. ii.) If firms cost curves don t change what will be the long-run price? What is the level of long-term profits? Assuming 10 firms enter the industry what is the new level of industry output? iii.) What is necessary for a long-run equilibrium in perfect competition? Identify the key assumption of the perfect competition model that shapes its long-run equilibrium. Page 4 of 5

5 iv.) In the graph on the bottom left show the effects on the industry supply and demand resulting from the changes in demand and supply. In the graph on the bottom right, show the new situation faced by the firm in perfect competition, again in the long-run equilibrium, again, assume that the firms cost curves have not changed. V. Profit Maximization Suppose that a perfectly competitive firm faces the following cost conditions: Quantity Total Supplied Fixed Variable Marginal Average Average Var. i.) The variable cost associated with the fourth unit of production is what? ii.) The minimum price that the firm will operate at in the short-run is what? iii) The minimum price that the firm will operate at in the long-run is what? iv) At the minimum price used for question 2 the firms profit would be what? v) At a price of $22 the profit maximizing level of production is what? vi) At a price of $22 the short run profit for the firm is what? vii) If total costs stay the same and all firms have the same cost conditions the long run price will be what? Page 5 of 5