Chapter 2 Supply, Demand, and Markets SOLUTIONS TO EXERCISES

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1 Firms, rices & Markets Timothy Van Zandt August 0 Chapter Supply, Demand, and Markets SOLUTIONS TO EXERCISES Exercise.. Suppose a market for commercial water purification systems has buyers with the following valuations (in 000s), from highest to lowest: Buyer 9 0 Valuation 9 0 These valuations are graphed in Figure E. and again in Figure E.. a. What is the total valuation of the first buyers? Illustrate this as the area under the valuation curve in Figure E.. Total valuation is =. See Figure E.. Figure E. (000s) Total valuation of first buyers Valuations 9 0 Buyer

2 Firms, rices & Markets Solutions for Chapter (Supply, Demand, and Markets) b. Suppose the price is. How much is the demand? How much is the total expenditure? How much is the surplus of each of the buyers? How much is the total consumer surplus? Illustrate the demand, the total expenditure, and the consumer surplus using the valuation curve in Figure E.. Demand is. Total values are as follows: See Figure E.. Expenditure = =, Consumer surplus = Valuation Expenditure = = 0. Figure E. (000s) Consumer surplus Total expenditure Valuations 9 0 Buyer

3 Firms, rices & Markets Solutions for Chapter (Supply, Demand, and Markets) Exercise.. Suppose there are buyers with valuations,,,,,,, and. a. Graph the valuations as points on the axes in Figure E., from highest to lowest. Figure S b. Suppose the market price is.0. How many buyers will purchase at this price? Connect the points on your graph so that it becomes a demand curve, and illustrate the quantity purchased when the price is.0. Four buyers will purchase, because this is the number of buyers whose valuations exceed.. Figure S =. demand d( )

4 Firms, rices & Markets Solutions for Chapter (Supply, Demand, and Markets) c. What is the total valuation of the buyers who would purchase when the price is.? Illustrate this as the area of a region on your graph. The total valuation of the top four buyers is =. Figure S Total valuation of first buyers d. What is the total expenditure by those who purchase? What is the total surplus? Illustrate these as the areas of regions on your graph. Total expenditure is. =. Total consumer surplus is =. Figure S Consumer surplus Total expenditure

5 Firms, rices & Markets Solutions for Chapter (Supply, Demand, and Markets) Exercise.. Recall the marginal valuation and marginal cost curves from Exercise.: Valuation: mv() = 00, Cost: mc() = 0 +. a. Invert them to find the formulas for the demand and supply curves: We solve = 00 for to obtain the demand curve and solve = 0 + for to obtain the supply curve: Demand: d( ) = 0 (/), Supply: s( ) = 0. b. Compute the equilibrium price by solving supply=demand. We find the equilibrium price by solving d( ) = s( ) 0 (/) = 0 0 = (/) 0 =. c. Compute the equilibrium quantity by substituting the equilibrium price into either the supply or demand curve at the equilibrium price, these are equal. = s(0) = 0 0 = 0 or = d(0) = 0 (/)0 = 0. d. Graph the demand and supply curves on Figure E.. Illustrate on the graph the equilibrium price and quantity, the consumer surplus, and the producer surplus. Figure E d( ) Consumer surplus s( ) 0 0 roducer surplus

6 Firms, rices & Markets Solutions for Chapter (Supply, Demand, and Markets) See Figure E.. e. Calculate the consumer surplus and the producer surplus. The triangle of the consumer surplus has base 0 and height 0. Hence, consumer surplus is (0 0)/ = 900. The triangle of the producer surplus has base 0 and height 0. Hence, producer surplus is (0 0)/ = 0. Exercise.. Consider the demand and supply curves from Exercise.. Assume a per-unit tax of is imposed. You are to find the price the buyers pay (including the tax), the price the sellers receive (net of the tax), and the quantity transacted. Some of the questions require that you graph curves within Figure E.. Figure E d( ) s Τ ( ) Consumer surplus Tax revenue Deadweight loss s( ) roducer surplus Τ a. You should find the new equilibrium values by shifting the supply curve, treating the tax as a cost born by the sellers. What is the supply s Τ ( ) as a function of the price including the tax? The new supply at the with-tax price is same as the old supply when the price was lower. Thus, the shifted supply curve is s Τ ( ) = s( ) =. b. Graph this function and the original supply curve s( ) on Figure E.. In which direction does the supply curve shift by? See Figure E.. The supply curve shifts U by ; it is really an upward shift in the marginal cost curve by. (With linear supply, it also looks like the supply curve shifted to the left. However, (a) the amount of this shift is not the amount of the tax and (b) with non-linear supply, the curve would shift up by but would not shift left by a fixed amount.)

7 Firms, rices & Markets Solutions for Chapter (Supply, Demand, and Markets) c. Calculate the equilibrium price paid by buyers (including the tax), price received by sellers (net of tax), and quantity. We find the market price paid by buyers by solving d( ) = s Τ ( ), 0 (/) =, = (/), 0 =. The amount retained by the sellers is less than this:. The quantity transacted is d(0) = s() =. d. Illustrate the equilibrium on the graph. Show the regions that correspond to (a) producer surplus, (b) consumer surplus, (c) tax revenue, and (d) deadweight loss. See Figure E..