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Simon Fraser University Spring 2016 Econ 302 Assignment 1 Due: in Lecture, Tuesday January 19, 2016. Show all your work. 1. (3 points) Suppose that the demand function for a good is D(p) = 100/p2 for p ≥ 0; D(p) is the units (the “number”) of people willing to buy the good when its price is p (i.e., their willingness-to-pay are greater than or equal to p). And suppose that the cost function of the monopolist is C(q) = 2q; C(q) is the cost of producing q units of the good. a Calculate the price elasticity of demand, (p): (p) = − dD(p)/D(p) . dp/p b Calculate the monopolist’s quantity and price. c Calculate the monopolist’s quantity and price, as well as the consumer’s price, when the government charges a sales tax of 12%. Assume that the sales tax does not affect the monopolist’s cost. d What is the price elasticity of demand if D(p) = C/p where C and are arbitrary positive constants? 2. (5 points) Suppose now that the demand function is linear: D(p) = 10 − p for p ∈ [0, 10] (and D(p) = 0 when p ≥ 10). And suppose that the cost function of the monopolist is still C(q) = 2q. a Calculate the price elasticity of demand, (p). The point of this exercise is to emphasize the the price elasticity of demand in general depends on the price, i.e., it is a curve. b Calculate the monopolist’s price and quantity. c Suppose that 3 months after the monopolist announced his price of p1 , he unexpectedly offers a discounted price of p2 < p1 , which was unanticipated by the market. The total profit of the monopolist is the revenue from selling at the price p1 , plus the revenue from 1 selling at the price p2 , and minus the total cost. Assume that people who bought the good three months ago would not want to buy it again. Calculate the optimal prices p1 and p2 that the monopolist should choose for this plan, and calculate the total quantity of sales. (Hint: since D(p) is the number of people with willingness-to-pay ≥ p, D(p2 ) − D(p1 ) is the number of people whose willingness-to-pay is in between p2 and p1 .) d How do p1 and p2 from part (c) compare with the monopolist’s price from part (b)? Does it make sense? 3. (2 points) Assume that the monopolist has a cost that is always increasing with the quantity produced: C 0 (q) > 0 for every quantity q. What happens to the monopolist’s quantity when the price elasticity of demand is always less than or equal to 1? Justify your answer from the first principle (i.e., the monopolist’s first order condition). 2