Problem Set 3 21 September 2007

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1 Eco 301 Name Problem Set 3 21 September Suppose that the U.S. demand and supply for soft drinks are given by Q D = P Q S = 4 P The price is in cents per can and quantity is in millions of cans per day. a. Using a ruler, graph the demand and supply lines for this market. Indicate at least two points on each line (such as their intercepts along the axes). (Let each line in the grid represent 10 cents along the price axis and 20 million cans along the quantity axis.) P Q b. Solve algebraically for the equilibrium price and quantity. How much do consumers spend on soft drinks per day (in millions of dollars)?

2 c. Calculate the price elasticity of demand at the equilibrium (using the equilibrium price and quantity as the base values ). Is demand elastic or inelastic? Explain briefly. d. Suppose that supply now becomes Q S = P. Has supply increased or decreased? Explain briefly. Calculate algebraically the new equilibrium price, quantity, and consumer expenditure. e. Has consumer expenditure gone up or down? Is this consistent with your finding about the price elasticity of demand at the initial equilibrium? Explain briefly. f. Now assume that the original supply and demand curves apply once more, but suppose that the government decides to levy an excise tax of 30 cents per can on soft drinks. Solve algebraically for the new equilibrium supply price (P S ), demand price (P D ), quantity transacted, and tax revenues. (You may wish to examine your diagram to see if your calculations make sense.)

3 g. Explain intuitively why the supply price, demand price, and quantity have changed as you found in part f. In particular, does the price paid by consumers go up by the amount of the tax per unit? Explain why or why not. Extra moral credit: (No worries: questions of this sort will not appear on examinations). Find the tax per can that would maximize tax revenues for the government. Find the supply price, demand price, quantity transacted, and tax revenues, given that tax per can.

4 2. Fenway Park is a relatively small park, and seating is limited to only 34,000. Hence, the number of tickets issued is fixed at that figure. (Assume for what follows that all seats are equally desirable and that all 34,000 are sold at the same price.) Seeing a golden opportunity to increase its revenue, assume the City of Boston has decided to levy a per ticket tax of $5, to be paid by the ticket buyer. Boston sports fans, a famously civic-minded lot, dutifully send in the $5 per ticket. Draw a well-labeled graph showing the impact of the tax. On whom does the tax burden fall buyers, sellers, or both? Why? 3. Harding Enterprises has developed a new product called the Gillooly Shillelagh. The market demand for this product is given as follows: Q = 240-4P a. At what price is the price elasticity of demand equal to zero? b. At what price is demand infinitely elastic? c. At what price is the price elasticity of demand equal to one? d. If the shillelagh is priced at $40, what is the point price elasticity of demand?

5 4. Suppose the demand curve for a product is given by Q = 10-2P + P S where P is the price of the product and P S is the price of a substitute good. The price of the substitute good is $2.00. (a) Suppose P = $1.00. What is the price elasticity of demand? What is the cross-price elasticity of demand? (b) Suppose the price of the good P increases to $2.00. Now what is the price elasticity of demand, and what is the cross-price elasticity of demand? 5. The inverse demand curve for product X is given by: PX = Q PY, where PX represents price in dollars per unit, Q represents rate of sales in pounds per week, and PY represents selling price of another product Y in dollars per unit. The inverse supply curve of product X is given by: PX = Q. a. Determine the equilibrium price and sales of X. Let PY = $10. b. Determine whether X and Y are substitutes or complements.

6 6. The market for digestive biscuits is described by the following equations: Q D = P and Q S = 2P. The Digestives Minister has decided that he wants to reduce the consumption of digestive biscuits as much as possible. The minister is considering either imposing a $40 per unit price ceiling or a per unit tax of $15 on consumers of digestives. a. What is the equilibrium price and quantity before any policy is imposed? b. Which of the two policies better achieves the minister s objective and why? c. Suppose the minister implements the $15 per unit sales tax on consumers. What is the government s revenue? d. Suppose the minister imposes a $15 per unit sales tax on producers instead of consumers. Compared to the tax on consumers, does the market price and quantity change? Explain. 7. Consider the market for rental housing in Boston. Suppose that all houses are equal in Boston and that the mayor wishes to assure that its citizens can afford housing. Consider the following two ways of pursuing this goal. For each method, predict what effect each proposal would have on the price and quantity of rental housing. Explain your answers carefully and illustrate graphically the changes that occur.

7 a. The mayor offers a subsidy to all builders of homes.(note: homes built are used for rental housing.) b. The mayor provides a subsidy directly to renters. c. Who gains and who looses from the implementation of policy a. and b.?