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Unformatted text preview: Department of Economics Fall 2007 University of California, Berkeley Prof. Gilbert Problem Set 1 Solution Sketches 1. Taxation. Let the market supply and demand for gasoline be given by Q S = 25 P- 45 and Q D = 105- 5 P , respectively, where Q represents millions of gallons per day. (a) Graph the supply and demand curves and indicate the equilibrium price and quantity. Find the consumer and producer surplus. To find the equilibrium price, set Q s = Q d , i.e. 25 P- 45 = 105- 5 P , and solve for P . The solution is P * = 5 , which corresponds to an equilibrium quantity Q * = 80 . Consumer and producer surplus are given by CS = 1 2 (21- 6)(80- 0) = 640 and PS = 1 2 (5- 1 . 8)(80- 0) = 128 . (b) The government tries to curb gasoline consumption by imposing a tax on consumers of 1.2 dollars per gallon of gasoline, collected at the pump. Find the equilibrium price and quantity. How much revenue does the government collect? What is the deadweight loss from the tax? Denote the price that producers charge be P . Denote the total amount of money that consumers pay for gasoline P d . Since P d = P + 1 . 2 , the quantity demanded is Q d = 105- 5 P d = 99- 5 P . Now it is easy. Get the equilibrium price by equating the quantity supplied and demanded, i.e. 99- 5 P = 25 P- 45 , so that P * = 4 . 8 and Q * = 75 . The government revenue is 1 . 2 * Q * = 90 . The deadweight loss is DWL = 1 2 (80- 75)(6- 4 . 8) = 3 . (c) Now consider a tax on producers of 1.2 dollars per gallon of gasoline sold. Find the equilibrium price and quantity. How much revenue does the government collect? Compare your answers to those of part (b). Denote the net revenue that producers receive (after tax) as P s . Given that P s = P- 1 . 2 , the new supply curve is Q s = 25 P s- 45 = 25 P- 75 . Now we can get the equilib- rium price by equating the quantity supplied and demanded, i.e. 105- 5 P = 25 P- 75 , so that P * = 6 and Q * = 75 . The government revenue and deadweight loss are the same as in part (b). 1 2. Monopoly pricing. A monopolist faces an inverse demand function P ( Q ) = 43- 4 Q where P is measured in dollars per unit. It has a constant marginal cost of 3 dollars per unit and a fixed cost of 19 dollars....
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This note was uploaded on 06/08/2008 for the course ECON 121 taught by Professor Woroch during the Fall '07 term at Berkeley.
- Fall '07
- Supply And Demand