Econ 100A Ans to PS2 - Department of Economics University...

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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 2 SOLUTIONS I. TRUE or FALSE and EXPLAIN : For each statement below, decide whether it is true or false, and explain the reasoning behind your answer in a few sentences . When appropriate, provide a diagram. 1. Francesca has a backward-bending labor supply curve because when she recently received an hourly wage increase, she voluntarily cut back on her hours—working fewer hours but earning the same amount. True. For a forward-sloped labor supply curve, we require that an increase in price (wage) would correspond to an increase in quantity (hours of labor – NOT money earned) supplied. Here, the price increase corresponded to a decrease in quantity supplied, hence the backward-bending labor supply curve. 2. If, in a two period world with a single good, consumption in the second period is a Giffen good , then the consumer will respond to a rise in the interest rate by saving less . True. The interest rate determines the relative prices of consumption in the two periods. To fix ideas, assume as we did in lecture that the nominal price of the consumption good (e.g., a loaf of bread) is $1 in both periods. The price of consumption in the second period, C 2 , is then 1/(1 + r). In that case, a rise in the interest rate lowers the price of C 2 . Because C s is a Giffen good, this lower price will result in lower consumption: C 2 falls. Necessarily consumption in the first-period consumption, C 1 , must rise. Remember that not all goods can be inferior, so since there are two goods in this story, and C 2 is inferior, C 1 must be normal. Increased C 1 automatically translates into decreased savings since savings is difference between money income and first period consumption. All of this can be shown in a picture: (1 + r’)I 1 (1 + r)I 1 I 1 C 2 C 1 C* 2 C* 1 r’ > r I.E Change in savings < 0 S.E.
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Econ 100A-Spring 2007 Page 2 PS2 Solutions 3. A firm that produces with labor and other inputs, and its technology exhibits decreasing returns to scale everywhere, will experience diminishing marginal returns to labor. False. Consider the production function (, ) Qf L K L K == + . Then the technology exhibits decreasing returns to scale everywhere because ( ,) f cL cK cL cK cL c K cf L K =+ <+ = for c>1. But, the technology trivially exhibits constant marginal returns to labor. 4. The two-input production function, Q = f(L,K) = (L 2 + K 2 ) ½ , exhibits constant returns to scale. True. To see this mathematically, pick a c>1 and observe that () 11 1 222 2 2 2 2 22 2 (, ) () ( ) ( ) ( f cL cK cL cK c L K c L K cf L K =+= + = . 5. Airports have a very inelastic demand for air traffic controllers. This implies that they find it hard to substitute computers for skilled controllers. True. Airport have an inelastic demand for air traffic controllers, they are not very sensitive to price changes for controllers. If the price of computers changes, then the relative price of skilled controllers also change. However, due to their inelastic demand, they won’t alter
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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 PS2 - Department of Economics University...

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