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p(q)=50-0.5q and cost curve=10q (the unit tax equilibrium Q=36) What is the ad valorem tax which...

p(q)=50-0.5q and cost curve=10q (the unit tax equilibrium Q=36)

What is the ad valorem tax which will generate the same quantity distortion?

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Homework Answers

Answer #1

p = 50 - 0.5q  

MR = 50 - q  

cost curve after ad valorem tax is

c = (1 + t)10q

where t is ad valorem rate

MC = 10(1 + t)

MR = MC (equilibrium condition or profit maximizing condition)

50 - q = 10(1 + t)  

50 - q = 10 + 10t  

50 - 10 - 10t = q  

40 - 10t = q  

Equilibrium quantity with per unit tax is Q = 36  

equilibrium quantity with ad valorem tax is q = 40 - 10t  

36 = 40 - 10t  

10t = 40 - 36

10t = 4

t = 4/10  

t = 40%  

so required ad valorem tax rate is 40%

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