Question

1 Production and Cost A firm has the production function $q = f(K, L) = (K^{1/3} + L^{1/3})^2$. The input prices of labour and capital are $w = 10$ and $r = 40$, respectively. (a) How much additional output does an additional (small) unit of capital produce? How much additional output does an additional (small) unit of labor produce? (b) Currently $K = 8$ and $L = 27$. Keeping output constant, how many more (small) units of capital do you need if you lose 18 (small) units of labour? (c) In the short run, the capital stock is fixed at 8. How much labour do you need to produce 81 units of output? What is the cost of producing this output? (d) In the long run, what ratio of capital to labour is cost minimizing? (e) In the long run, what is the lowest possible cost to produce 81 units of output?

          1 Production and Cost
A firm has the production function $q = f(K, L) = (K^{1/3} + L^{1/3})^2$. The input prices of labour and
capital are $w = 10$ and $r = 40$, respectively.
(a) How much additional output does an additional (small) unit of capital produce? How much
additional output does an additional (small) unit of labor produce?
(b) Currently $K = 8$ and $L = 27$. Keeping output constant, how many more (small) units of capital
do you need if you lose 18 (small) units of labour?
(c) In the short run, the capital stock is fixed at 8. How much labour do you need to produce 81
units of output? What is the cost of producing this output?
(d) In the long run, what ratio of capital to labour is cost minimizing?
(e) In the long run, what is the lowest possible cost to produce 81 units of output?

1 Production and Cost
A firm has the production function q = f(K, L) = (K^1/3 + L^1/3)^2. The input prices of labour and
capital are w = 10 and r = 40, respectively.
(a) How much additional output does an additional (small) unit of capital produce? How much
additional output does an additional (small) unit of labor produce?
(b) Currently K = 8 and L = 27. Keeping output constant, how many more (small) units of capital
do you need if you lose 18 (small) units of labour?
(c) In the short run, the capital stock is fixed at 8. How much labour do you need to produce 81
units of output? What is the cost of producing this output?
(d) In the long run, what ratio of capital to labour is cost minimizing?
(e) In the long run, what is the lowest possible cost to produce 81 units of output?

Added by Ricardo M.

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