ECN344 PS1 - questions problem set 1 PDF

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ECN 344 Economics of Technology and Innovation Problem Set 1

1. (Church & Ware, page 44, problem 4) During the Enlightenment, the City of Calgary had a more-or-less free market in taxi services. Any respectable firm could provide taxi service as long as the drivers and cabs satisfied certain safety standards. Let us suppose that the constant marginal cost per trip of a taxi ride is $5 and that the average taxi has a capacity of 20 trips per day. Let the demand function for taxi rides be given by D(p) = 1100 − 20p, where demand is measured in rides per day, and price is measured in dollars. Assume that the industry is perfectly competitive. (a) What is the competitive equilibrium price per ride? What is the equilibrium number of rides per day? What is the minimum number of taxi cabs in equilibrium? (b) During the Calgary Stampede (The Greatest Outdoor Show on Earth), the influx of tourists raises the demand for taxi rides to D(p) = 1500 − 20p. Find the following magnitudes, based on the assumption that for these 10 days in July, the number of taxicabs is fixed and equal to the minimum number found in part (a): equilibrium price; equilibrium number of rides per day; profit per cab. (c) Now suppose that the change in demand for taxicabs in part (b) is permanent. Find the equilibrium price, equilibrium number of rides per day, and profit per cab per day. How many taxi cabs will be operated in equilibrium? Compare and contrast this equilibrium with that of part (b). Explain any differences. (d) With care and precision on one diagram, graph the three different competitive equilibria found in parts (a) through (c). In each case identify the supply curve, the demand curve, and the equilibrium price and quantity. 2. (Church & Ware, page 44, problem 5) Suppose that there are 95 taxicabs and that the City of Calgary decides that it is time to enter the Industrial Age and provide its citizens with an alternative mode of transportation: light rail transit (LRT). The new demand curve for taxi rides is D(p) = 1000 − 20p + 1000f , where f is the fare per LRT ride, measured in dollars. Suppose that the city council sets f = $1.00. (a) Find the short-run competitive equilibrium: the price per ride, number of rides per day, and the profit per cab per day. Is the taxicab market in long-run equilibrium? (b) Suppose the City of Calgary increases the LRT fare to $2.00. What are the new short-run and long-run equilibria?

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(c) Suppose the City of Calgary decreases the LRT fare to $0.50. What are the new short-run and long-run equilibria? 3. (Church & Ware, page 44, problem 6) Suppose that demand for rollerblades is given by D(p) = A − p. The cost function for all firms is C(y) = wy 2 + f , where f is a fixed set-up cost. The marginal cost of production is MC(y) = 2wy. Assume that the industry is perfectly competitive. (a) Find a competitive firm’s supply function. If there are n firms in the industry, what is industry supply? (b) If there are n firms in the industry, find expressions for the competitive equilibrium price and quantity. What is the equation for how much each firm produces? What is the equation for the profit of each firm? [Hint: Your answer should be 4 algebraic equations that express the endogenous variables (price, quantity, firm supply, and firm profit) as a function of the exogenous variables (A, n, f , and w).] (c) Suppose A = 100, w = $4, f = $100, and n = 2. Using the equations you derived in part (b), what is the equilibrium price and quantity? Firm supply and profits? Using two diagrams, graph this competitive equilibrium. In one diagram illustrate the market equilibrium. In the second, show the equilibrium position of a representative firm. On this second diagram make sure you indicate the profit-maximizing output of a firm as well as the profit earned. (d) Is the equilibrium you found in part (c) a short-run or long-run equilibrium? Why? If the industry is not in long-run equilibrium, explain the adjustment process that will occur. (e) For the parameter values given in part (c), find the long-run competitive equilibrium. On the two diagrams from part (c), indicate the long-run equilibrium. What is the long-run equilibrium number of firms?

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