1. Given the production function Q = f(L,K) = KL2 – L3 , where Q is output and L and K are the labor and capital inputs, respectively. Suppose K is a fixed input set at 15 units. Mathematically and graphically show the input levels that divide stages I & II and stages II & III of production.
1. Given the production function Q = f(L,K) = KL2 – L3 , where Q is output and L and K are the labor and capital inputs, respectively. Suppose K is a fixed input set at 15 units. Mathematically and graphically show the input levels that divide stages I & II and stages II & III of production.
2.Consider the production functions for X and Y given below.
X = 2K2 + 4L ; Y = 10K0.5 L0.5 ; Suppose the isocost equation is given by C = 4L + 10K, derive (i) the long-run cost function for good Y and (ii) the short-run cost function for good X if 10 units of capital are employed in X.
3. Given: Q = 100K0.6L0.8; w = 50; r = 80; Q0 = 2,000. Graphically illustrate the expansion path for the firm if it decides to increase its target output to Q1 = 4,000.
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