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Intermediate Microeconomics Assignment

Question 1: In class, we discussed how a competitive market reaches a long-run competitive equilibrium when the market was initially very profitable. Graphically depict the transition of a market to a long-run competitive equilibrium if the market is initially not profitable. To receive full credit, you must: 1. Show a firm-level graph correctly depicting profit in the short run and long run. 2. Show a market-level graph correctly depicting the long-run supply, the demand, the initial short-run supply and the final short-run supply. 3. All prices and quantities necessary to fully understand the graphs. 4. A story detailing how and why the transition to the long-run competitive equilibrium occurred. Question 2: Suppose that you open the first firm in a new industry, and that production in this industry has inherently very high fixed costs. The industry’s demand function and your firm’s cost function are given by: D(p) = 300 − (1/4)p C(q) = q2 50; 000 a) State the industry’s inverse demand function. b) Being the only firm in the industry, assume that you act as a monopolist. Find the profit-maximizing quantity and price, and find your profit. c) We know that in a competitive market, the market price is determined where the industry’s supply curve equals the industry’s demand curve. Find the price in this market if your firm chooses to price competitively. d) Finally, find your firm’s profit if you decide to price competitively. Based on the profit you found, will there be any competitive entry into this market or are you a natural monopoly? Why? Question 3: Suppose that you are putting on a wine-tasting festival for the bourgeoisie of Eugene. Having done extensive research into the characteristics of each possible attendant and the costs to provide to each attendant, you come to the following conclusions about your costs and each individual’s demand: D(p) = 200 − (1/2)p C(q) = 20q where C(q) is the cost to provide q samples of wine and D(p) is each consumer’s demand for wine samples given the price you set p. Because your wine-tasting festival is so far superior to every other festival in the area, you essentially have monopoly over each attendant. a) Calculate the profit you would earn if you priced each sample of wine monopolistically, and state the price per wine sample and total number of samples each consumer will have. If the number of wine samples shocks you, just remember that people spit wine out at wine tastings. b) Suppose further that you decide that you want to charge an entry fee into the winetasting festival. Given that you are still pricing wine samples monopolistically, what is the highest ticket price you can charge the bourgeoisie of Eugene? c) What is the total profit (from both the ticket and the sale of wine samples) you expect to earn from each attendant if you charge the maximum possible ticket price? Having taken an intermediate economics course and paid close attention to the discussion on a two-part tariff, you know that charging a monopolistic price for each wine sample and a ticket price will not maximize profits. Instead, it is better to charge a competitive rate for each wine sample and an enormous ticket price. d) Find the competitive price for a single wine sample. 6e) Given the competitive price for each wine sample, what is the highest ticket price you can charge the bourgeoisie of Eugene? f) Is this arrangement more profitable than the strategy in parts (a)-(c)? Intuitively describe why this is, hearkening to the forgone profit in parts (a)-(c). A graph may help your explanation. Question 4: Suppose that you are a national retailer of shoes, and you produce all your shoes in one small town in the middle of Nebraska. Because the national market is quite large, you must sell your shoes at the competitive market price of $64. However, being the only company in the small town, you have the power to set a non-competitive wage for all the workers you hire. The town’s labor supply function and your production function are given by: S(w) = 1/2w f(x) = px where w is the wage you set in the town, x is the number of workers you choose to hire. a) Find the town’s inverse supply function. b) Using the inverse supply function you found in part (a), state your firm’s profit function. c) Find the profit-maximizing quantity of shoes to produce, workers to hire, and wage to pay the workers. d) Find the optimal profit.

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