ps4_s04 (ans)

# ps4_s04 (ans) - Econ 313 Spring 2004 PS#4-XtraQ ANSWERS 1...

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1. Given: x Fred = (KL) 1/2 x Ted = (KL) 2 Ima is a dope. It’s clear that Ted has the superior technology! Note that Ted has increasing returns to scale and Fred has merely constant returns to scale. Try some numbers and note that Ted always gets a lot more produced than does Fred with the same amount of inputs. Also, if you calculate the cost functions you will see that Ted’s cost functions are superior to Fred’s. If I were you I would do this. Find the long-run total cost curve for each and compare them. You should get that Ted’s lrtc curve is concave and Fred’s in linear. And when you plot them, Ted’s should be everywhere below Fred’s.
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Unformatted text preview: 2. Firm 1 and Firm 2 use the same type of production function, but Firm 1 is only 90% as productive as Firm 2. That is, the production function of Firm 2 is x 2 = f(K, L) and the production function of Firm 1 is x 1 = 0.9f(K, L). At a particular level of inputs, how does the marginal product of labor differ between the firms? The marginal product of labor for Firm 1 is only 90% of the marginal product of labor for Firm 2 for a particular level of inputs. Using calculus we find that the MP L for Firm 1 is ∂ x 1 / ∂ L = 0.9 ∂ f(L, K)/ ∂ L = 0.9 ∂ x 2 / ∂ L Econ 313 - Spring 2004 PS#4-XtraQ - ANSWERS...
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