Suppose a firm’s total cost is C = rK + (q 2 /2K), where K = the firm’s capital (plant size), q is output and r is the price of a unit of capital. 1. What is short-run average total cost (C/q) and what is marginal cost dC/dq, assuming K is fixed at K0 (2 points) 2. Suppose K is not fixed, but output is fixed at q0. Given this exogenous output and exogenous price of capital r0, what level of capital (K*) is most efficient – that is, minimizes total cost C? Do not forget to check the second order condition (4 points) 3. Find and interpret ∂K*/∂r.

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Short-Run Costs and Long-Run Costs

Cost of short-run and the long-run is an economic term that describes the cost involved in the production of goods in a firm in the short as well as long period.