200a_f08_ps_6_ak

200a_f08_ps_6_ak - University of California, Davis ARE/ECN...

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Unformatted text preview: University of California, Davis ARE/ECN 200A Fall 2008 Joaquim Silvestre & Shaofeng Xu PROBLEM SET 6 ANSWER KEY 1. Deadweight Loss in a Subsidy The amount T of a lumpsum tax that, together with the quantity subsidy, puts the consumer at the same utility level as in the situation with no taxes or subsidies is the number T that solves the equation: v ( p 1 ; w & T ) = u v ( p ; w ) ; i.e., w & T = e ( p 1 ; u ) ; or & T = e ( p 1 ; u ) & w = & CV [ p ; p 1 ] : On the other hand, the total actual amount of subsidy under the quantity subsidy and lumpsum tax is s ~ x 1 ( p 1 ; w & T ) = s ~ x 1 ( p 1 ; w & CV [ p ; p 1 ]) = s h 1 & p 1 & s; p & 1 ; u : Hence, the desired measure of deadweight loss is DL 2 [ s ] s ~ x 1 & p 1 ; w & T & T = s h 1 & p 1 & s; p & 1 ; u & CV p ; p 1 = s h 1 & p 1 & s; p & 1 ; u + e & p 1 ; u & e & p ; u : Figure 1 graphically respresents the case where good 1 is normal at ( p; w ) and there is substitution. The amount s h 1 & p 1 & s; p & 1 ; u is the area of the rectangle with base h 1 & p 1 & s; p & 1 ; u and height s; whereas CV [ p ; p 1 ] = w & e ( p 1 ; u ) = e ( p ; u ) & e ( p 1 ; u ) = R p 1 p 1 & s h 1 & p 1 ; p & 1 ; u dp 1 is the area below(i.e., to the left of) the Hicksian demand curve at utility level u and with lower (resp. upper) limit of integration equal to p 1 & s (resp.(resp....
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200a_f08_ps_6_ak - University of California, Davis ARE/ECN...

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