Market Structures and Pricing Decisions Applied Problems.

Feb 3rd, 2012
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Market Structures and Pricing Decisions Applied Problems. Please complete the following two applied problems: Problem 1: Robert’s New Way Vacuum Cleaner Company is a newly started small business that produces vacuum cleaners and belongs to a monopolistically competitive market. Its demand curve for the product is expressed as Q = 5000 – 25P where Q is the number of vacuum cleaners per year and P is in dollars. Cost estimation processes have determined that the firm’s cost function is represented by TC = 1500 + 20Q + 0.02Q2. Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary. What are the profit-maximizing price and output levels? Explain them and calculate algebraically for equilibrium P (price) and Q (output). Then, plot the MC (marginal cost), D (demand), and MR (marginal revenue) curves graphically and illustrate the equilibrium point. How much economic profit do you expect that Robert’s

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Problem 1:When the demand function is Q = 5,000 - 25P, the inverse demand function isP = 200 - 0.04QTR = (P)(Q)= 200Q - 0.04Q2MR = 200 - 0.08QTC = 1500 + 20Q + 0.02Q2MC = 20 + 0.04QProfit is maximized when MR = MC200 - 0.08Q = 20 + 0.04QOr, 0.12Q = 180Or, Q* = 180/0.12 = 1500Therefore P* = 200 - (0.4*1500) = 200 - 60 = 140Profit = TR - TC = 210000 - 76500 = 133500. Therefore, in the first year it will be earning a profit of $133500.Getting attracted by this profit other firms outside the industry will be attracted and enter the industry. As more and more firms enter the industry, the number of products available to a consumer will increase. The demand curve for each firm will shift to the left. Again, if the firms were incurring losses in the short run, few firms will go out of the industry which will lower the consumers' choice and shift the demand curve faced by each firm to the right. This process of entry and exit will continue till firms are earning zero profit.Problem 2:Pg = 1900Pb = 2100G = 9960 = 60%B = 6640 = 40%GGC has substantial excess capacity-it could easily install 25,000 systems annuallyQw =2100 - 6.25Pgw + 3Pbw + 2100Ag - 1500Ab + 0.2Yw = 2100 - 6.25 Pgw + (32100) + (21001.5) - (15001.2) + (0.260000) = 21750 - 6.25 PgwQe = 36620 - 25Pge + 7Pbe + 1180Ag - 950Ab + 0.085Ye = 36620 - 25 Pge + (72100) + (11801.5) - (9501.2) + (0.08530000) = 54500 - 25 PgeQw = 21750 - 6.25 PgwOr, Pgw =

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