Question

each of the production functions below, calculate the least cost of producing unit of output for the given input prices. (a) 4 - *1 + 2x2; (wi, W2) - (1.4) $ Explain your reasoning. One unit of output can be produced either with 1 unit of input 1 costing $0 , or half of a unit of input 2, costing $ . (b) $ 4 = min{2X1 + X2, X3}; (W1, W2, W3) = (2, 4, 4) 5 Explain your reasoning. Define a composite input, z = 2x1 + x2. Then q = min{z, X3} and one unit of output can be produced with one unit of input z and one unit of X3. One unit of z can be produced with half a unit of X1 costing $1, or one unit of X2 costing $4. One unit of X3 costs $ 4 . Therefore, the least cost of producing one unit of output is $ 5 . 4 = min{X1, X2} + X3; (W1, W2, W3) = (4, 3, 6) (c) $ Explain your reasoning. Define a composite input z = min{X1, X2}. Then q = 2 + x3, so one unit of output can be produced with one unit of z or one unit of X3. The former which requires one unit of X1 and one of x2 costs $ ; the latter costs $ .

Answer 1

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