# PS6_Answers - TRUE OR FALSE 1. The marginal product of a...

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TRUE OR FALSE 1. The marginal product of a factor is just the derivative of the production function with respect to the amount of this factor, holding the amounts of other factor inputs constant. TRUE by definition, check the notes. 2. If a profit-maximizing competitive firm has constant returns to scale, then its long-run profits must be zero. TRUE since with constant returns to scale, I can double production by exactly doubling the amount of inputs and thus doubling the cost. Let’s say that the firm’s level of profits is equal to K. Then, since profits are given by py-cost=K, if the firm doubles production to 2y thus doubling costs to (2costs) profits are: p(2y) – (2cost)=2(py-cost)=2K it doubles its profits so it has an incentive to double again and so on, unless K=0 in which case it makes no difference. 3. If the supply curve is vertical, then the amount supplied is independent of price. TRUE by definition since a vertical supply curve means that the supply is fixed regardless of price (see graph in class). 4. The demand curve, which is a downward-sloping straight line, crosses the supply curve, which is an upward-sloping straight line. If a tax is introduced where sellers must pay a tax of \$2 per unit sold, then the equilibrium price paid by demanders will rise by more than \$1 if the absolute value of the slope of the demand curve is greater than the absolute value of the slope of the supply curve. TRUE, let (inverse) demand be P=a-bQ and the (inverse) supply is P=c+dQ. Notice that the absolute value of the slope of the demand curve is b and the absolute value of the slope of the supply curve is d (assuming they are both positive) . To save ourselves some steps I’ll solve for Q on both supply and demand first (but you can do it first equating prices and get the same answer): Q=(a/b)-(1/b)P for demand and Q=(1/d)P-(c/d). When there are no taxes we have (a/b)-(1/b)P=(1/d)P-(c/d), solving for P we get that the equilibrium price is: P=(ad+bc)/(b+d) Now we introduce a tax so P s =P d -t= P d -2. In equilibrium we have (a/b)-(1/b)P d =(1/d)P s - (c/d), replacing P s =P d -2 into the equilibrium condition we have (a/b)-(1/b)P d =(1/d)P d -(c/d)- (2/d) which, solving for P d , gives that in the presence of a \$2 sales tax the price paid by the consumer is P d = [(ad+bc)/(b+d)]+[2b/(b+d)] The difference between both prices is given by P d -P=2b/(b+d) which will be larger than one if 2b/(b+d)>1, if 2b>(b+d), if b>d which is what the question states: the price increase will be larger than one if the slope of the demand curve is larger than the slope of the supply curve.

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MULTIPLE CHOICE 1. A competitive firm produces output using three fixed factors and one variable factor. The firm’s short-run production function is q = 305 x - 2 x 2 , where x is the amount of variable factor used. The price of the output is \$2 per unit and the price of the variable factor is \$10 per unit. In the short run, how many units of x should the firm use? a.
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## This note was uploaded on 07/28/2010 for the course ECON 301 taught by Professor Hansen during the Fall '08 term at University of Wisconsin.

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PS6_Answers - TRUE OR FALSE 1. The marginal product of a...

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