Fall2008_Midterm1_P2_sol

Fall2008_Midterm1_P2_sol - Problem Consider the following...

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Problem Consider the following market for bananas: P B D = 1 Q B D ; P B S = Q B S : (A) Calculate the equilibrium price and quantities demanded and supplied for the bananas. Since supply and demand prices and quantities will be equal in a market equilibrium, we can set P ± P B D = P B S and Q ± Q B D = Q B S . Solving for Q : P = 1 Q ; P = Q ) 1 Q = Q ) 2 Q = 1 ) Q = 1 2 : Since P = Q , it follows that P = 1 2 : (B) Find total surplus. CS PS S D 0.5 0.5 P Q The consumer surplus is the triangle marked CS in the diagram. Calculating the area of the triangle: CS = (1 1 2 ) ² 1 2 ² 1 2 = 1 8 : The producer surplus is the triangle marked PS in the diagram. Calculating the area of the triangle: PS = ( 1 2 0) ² 1 2 ² 1 2 = 1 8 : The total surplus is the sum of the consumer and producer surpluses: TS = CS + PS = 1 8 + 1 8 = 1 4 : 1
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(C) Now assume that the government imposes a 50 cent subsidy. Recalculate the equilibrium price and quantities demanded and supplied. Since prices are free to adjust so that the market clears, we have that
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Fall2008_Midterm1_P2_sol - Problem Consider the following...

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