Solutions_to_PS_2

Solutions_to_PS_2 - Q D = 1 P . What price will maximize...

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ECON W3211.002 Intermediate Microeconomics Problem Set 2 Due Monday, September 27, 2010 1. Perloff, Problem 3.11 (a) In a very short run the supply curve is fixed (vertical supply curve). In this case, shift in demand only changes the price, but quantity remains the same. Thus Δ Q Q = 0 , and hence η SL = 0 . (b) As salary remains high, more graduate students will be attracted to phd program. In the long run, supply curve will be more elastic. Thus η LL > 0 . 2. Let Q = AP ± be a demand curve, where A > 0 and ± < 0 . (a) What is the price elasticity of demand? : ± = P Q dQ dP = P AP ± ±AP ± - 1 = ± . (b) Revenue is the price of a good times the quantity sold of that good, i.e., R = P × Q . Assume A = 1 and ± = - 1 . Let Q s = 4 P be a supply curve. What is the equilibrium price, quantity and revenue? : P * = 1 2 , Q * = 2 , and R * = 1 . (c) Now suppose that the supply curve shifts to Q s = 4 P - 3 . What is the equilibrium price, quantity and revenue? : P ** = 1 , Q ** = 1 , and R ** = 1 . (d) Recall that
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Unformatted text preview: Q D = 1 P . What price will maximize revenue? : Revenue is P × D ( P ) = 1 , regardless of the price, so all prices maximize revenue. 3. Suppose the supply and demand curves for gasoline are given by Q D = 9-1 4 P Q S = 2 P (a) What is the equilibrium price and quantity? : P * = 4 and Q * = 8 . (b) What is the price elasticity of demand and supply at the equilibrium? : ± = P Q dQ D dP = 4 8 (-1 4 ) =-1 8 and η = P Q dQ S dP = 1 2 2 = 1 . (c) Suppose the government impose a $0.9/gallon tax on gasoline, paid by buyers. Solve for the new equilibrium. What portion of the tax is is paid by consumers, and what portion by sellers? : P D-t = P S , where t = 0 . 9 , hence 9-1 4 P D = 2 P s = 2( P D-. 9) which implies P D = 4 . 8 and P S = 3 . 9 . After tax quantity is 7 . 8 . 1...
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This note was uploaded on 10/03/2011 for the course ECON W3211 taught by Professor Elmes during the Fall '09 term at Columbia.

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