PS 06 - 3 If there are two factors of production L and K...

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Dr. Steven Waters Econ 380 Page 1 of 1 Problem Set #6 Production 1) Digging clams by hand in Sunset Bay requires only labor input ( L ). The total number of clams ( q ) obtained per hour is given by: 2 1 100 L q = a) Graph the relationship between q and L b) Calculate the AP L c) Graph AP L d) Calculate the MP L e) Graph MP L f) Show that the L L AP MP < for all positive values of L. Explain why this is so. 2) Suppose the production function is: 2 1 2 1 L K q = a) Calculate AP L and AP K (Note that they will be functions of both K and L ) b) Graph the AP L curve for K=100. c) Calculate the MP L and graph it assuming K=100. . d) Does this production function exhibit diminishing MP L ? e) For this production function, show that L L AP MP 5 . 0 = . f) Calculate the rate of technical substitution RTS L,K
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Unformatted text preview: 3) If there are two factors of production, L and K , and 3 / 1 4 / 1 5 K L AP L βˆ’ β‹… ≑ , what is the formula for ? K MP (Yes, I did mean the marginal product of capital.) 4) Suppose , 1 ) ( ) , ( / 1 β‰  ≀ + = = ρ L K L K f q a) Show that this function exhibits constant returns to scale b) Calculate L K MP MP and c) Calculate RTS L,K d) Calculate the output elasticity K q , Ξ΅ 5) Euler’s Theorem implies that for a constant returns-to-scale production function of the form ) , ( L K f q = , L f K f q L K β‹… + β‹… = . Use this result to show that for a constant returns-to-scale production function, if L L AP MP > then K MP must be negative....
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