PS13+homework+solutions - Intermediate Microeconomics 2010...

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Intermediate Microeconomics, 2010 Problem Set 13: Homework Solutions 1. Taxes. Consider the following quasilinear economy: U ( m;q ) = m + 54 p q c ( q ) = 1 2 q 2 and Y = 100 . Recall that we found the competitive allocation to be [ q ± ;q ± ± ;m ± ] = [9 ; 9 ; 81 2 ; 19] and p ± = 10 on a previous problem set. Now we will consider the consequences of a tax: What happens with a tax t = 9 : 5 which has to paid by the ±rm? What is the competitive allocation with a tax, x t = [ q t ;q t t ;m t ] . (Hint: q t is going to be 3 , 4 , 5 or 6 . Try each one.) What is the tax revenue T ? What is the deadweight loss? (Hint: Follow the steps used in the exercise.) I will drop the t superscript for convenience. The new condition is now v 0 ( q ) = c 0 ( q ) + t: This means that 54 2 q ² 1 = 2 = q + 9 : 5 ; which means that q ± = 4 : Now we will ±nd the prices: p ± C = c 0 ( q ± ) + t = 4 + 9 : 5 = 13 : 5 p ± F = p ± C ± t = 13 : 5 ± 9 : 5 = 4 This allows us to get pro±ts and money holdings: ± ± = 4 ² 4 ± 1 2 4 2 = 8 m ± = Y ± p ± ² q ± = 100 ± 13 : 5 ² 4 = 46 The tax revenue is T = 9 : 5 ² 4 = 38 and DWL = TS ( q = 9) ± TS ( q = 4) = ± 54 p 9 ± 1 2 9 2 ² ± ± 54 p 4 ± 1 2 4 2 ² = 43 2 Now we do it the hard way. With a tax
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