ps 4 solutions

ps 4 solutions - Intermediate Microeconomics Summer 2007...

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1 Intermediate Microeconomics Monika Thomas Summer 2007 Solutions: Problem Set 4 10.2 With a $3 tax, setting d s Q Q = implies 10 .5( 3) 2 7 s s s P P P - + = - + = Substituting into the equation for d P implies 10 d P = . Substituting this price into the equation for quantity demanded implies 5 Q = million. At these prices and quantities, consumer surplus is $25 million, producer surplus is $12.5 million, and government tax receipts are $15 million. The deadweight loss is $1.5 million. The deadweight loss measures the difference between potential net benefits ($54 million) and the net benefits that are actually achieved ($25 + $12.5 + $15 = $52.5 million).
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2 10.5 Using the supply and demand curves from Example 10.1 and an excise tax of $0.40 implies 165 50( 0.40) 66 55 0.75 s s s P P P - + = + = Substituting into the equation for d P implies 1.15 d P = . Substituting s P into the supply equation implies 66 55(0.75) 107.40 Q = + = . Finally, the government tax receipts will be 0.40(107.40) 42.95 tQ = = . These values correspond with those in Table 10.1. Graphically, the solution is 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0 50 100 150 200 250 Quantity Price Supply Supply + 0.40 Demand
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3 10.7 a) With perfectly elastic supply, a $4 excise tax shifts the supply curve up as pictured below. Consumers will bear the entire burden of the tax. The end result is that the equilibrium quantity falls from Q 1 to Q 2 , the price producers receive remains the same ($60), and the price consumers pay rises from $60 to $64. Q 2 Q 1 Q P $64 $60 S + $4 S D b) When supply is perfectly inelastic, producers will bear the entire burden of the tax. Since supply is inelastic, it is easiest to think about this problem graphically as shifting down the demand curve. [Convince yourself you’d get the same result had we
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ps 4 solutions - Intermediate Microeconomics Summer 2007...

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