PS3sol - Problem Set 3 Solutions Applications of the...

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Problem 1 Quantity demanded equal quantity supplied. Q D ( P D ) = Q S ( P S ) P S = P D t Therefore, Q D ( P D ) = Q S ( P D t ) Totally di/erentiate with respect to t dQ D dP D dP D dt = dQ S dP S ( dP D dt 1) Rearrange dP D dt = dQ S dP S = ( dQ S dP S dQ D dP D ) When the initial value of the tax is zero dP D dt j t =0 = dQ S dP S P S Q S = ( dQ S dP S dQ D dP D ) P S Q S = dQ S dP S P S Q S = ( dQ S dP S P S Q S dQ D dP D P D Q D ) Thus, dP D dt j t =0 = S ( S D ) Problem 2 a) To ±nd the equilibrium price and quantity, we set quantity demanded equal quantity supplied Q D = Q S Q D = 100 2 P D ; Q S = 20 + 6 P S ; P S = P D = P 100 2 P = 20 + 6 P P = 10 ; Q = 80 b) With a tax of $4 per unit, P S = P D 4 Q S = 20 + 6 P S = 20 + 6( P D 4) = 6 P D 4 In equilibrium, Q D = Q S 100 2 P D = 6 P D 4 The price consumers pay P D = 13 The price ±rms receive
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PS3sol - Problem Set 3 Solutions Applications of the...

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