Econ 100A Ans to PS3 - Department of Economics University...

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Econ 100A-Spring 2007 Page 1 Problem Set 3 Answers D e p a r t m e n t o f E c o n o m i c s Spring 2007 University of California, Berkeley Prof. Woroch Economics 100A PROBLEM SET 3 SUGGESTED ANSWERS TRUE or FALSE or UNCERTAIN and EXPLAIN : For each statement below, decide whether it is true or false or cannot be determined given the information, and explain the reasoning behind your answer in a few sentences. When appropriate, provide a diagram. 1. Worried that too many people are smoking in California, Gov. Schwarzenegger is correct in his welfare economic analysis by favoring a law that imposes an ad valorem tax on cigarette sales, rejecting a corporate income tax on tobacco companies. Solution : True. Recall the equation for profits with no corporate income tax: π =×− p qc q () . The profit-maximizing level of output, q * , satisfies : d dq pcq =⇒ − = 00 '( ) * (i.e., price = marginal cost) Now consider the equation for profit with a corporate income tax of τ : πτ =− × ( ( ) ) 1 pqc q The profit-maximizing level of output with the corporate income tax, q * , satisfies : d dq q q ττ ⇒ = 01 0 ( ) ( ' ) ' ** * * Therefore, the corporate income tax has no effect on market output. This means that there is no effect on the supply curve. Hence, there is no change in producer surplus. Since the corporate income tax does not affect the demand curve, social welfare is unchanged. Now consider the ad valorem tax. Let this be denoted by t. Suppose a given individual consumes 2 goods: cigarettes (C) and beer (B). An ad valorem tax on cigarettes causes the marginal rate of transformation to change from p p C B to pt p C B 1 + . Assume cigarettes are a normal good. This would cause consumers to reduce their consumption of cigarettes. Hence, market demand would fall reducing the equilibrium number of cigarettes sold in the market. This is shown in the diagram below. As can be seen, the shift in demand causes the market equilibrium to change, thus creating deadweight loss.
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Econ 100A-Spring 2007 Page 2 Problem Set 3 Answers 2. If a consumer has a quasi-linear demand utility function for only two goods in the world, movies and music, then income effects on movies will be zero. Solution: Uncertain. Let x denote movies and y denote music. With quasi-linear utility, () ( , ) ( ) 1 u x yv x by =+ or () (,) () 2 u x yb x vy = + . In the first case, it is easy to see that the optimal number of movies to see satisfies vx b p p x y '( ) * = . Since income (I) does not enter this expression, income effects on movies will be zero. In the second case, the optimal number of movies to see is x Ip y p y x * * , = where the optimal consumption of music satisfies b vy p p x y '( ) * = . Therefore, x x * => 1 0 . In other words, there will be income effects on movies. 3. If, in the short run, a firm has sunk costs, then these costs would not be deducted from revenue to find its producer surplus, and so its producer surplus is greater than economic profit.
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This note was uploaded on 07/15/2010 for the course ECON 100A taught by Professor Woroch during the Spring '08 term at University of California, Berkeley.

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Econ 100A Ans to PS3 - Department of Economics University...

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