hw4 - x (resp. MPy) increase, stay the same, or decrease,...

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Eco 300 Homework 4, due Thursday 03/31 . There are two problems and total points equal 40. 1. (20 points) Fill out the blank fields in the table below as required. For each production function, columns 2 and 3 (MP x and MP y ) are the marginal products. Fill out the rest of the table as follows: In column 4, fill in the expression for the marginal rate of technical substitution (MRTS x,y ). In column 5 (Scale effects) fill in IRS, CRS, or DRS depending on whether the production function exhibits increasing, constant, or decreasing returns to scale . In columns 6 and 7, fill in I, C, or D depending on whether each input (x or y) exhibits increasing, constant or decreasing marginal returns (i.e. will MP
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Unformatted text preview: x (resp. MPy) increase, stay the same, or decrease, when x (resp. y ) increases?). Production functions MP x MP y MRTS x,y Returns to Scale Marginal Return to x Marginal Return to y 2x + 3y 2 3 x 1/2 y 1/2 y 1/2 / 2x 1/2 x 1/2 / 2y 1/2 x 1/4 y 1/4 y 1/4 / 4x 3/4 x 1/4 / 4y 3/4 x 2 y 2xy x 2 x + y 1/2 1 1 / (2y 1/2 ) 2. (20 points) A firm has a Cobb-Douglas production function Q = L 2 K 2 . The marginal products for this production function are: MP L = 2LK 2 , MP K = 2L 2 K. Suppose the price of labor is w = 10 per unit and the price of capital is r = 1 per unit. Find the cost-minimizing input choice if the firm wants to produce 121,000 units of output....
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