Consider the firm Plainview Oil, which produces barrels of oil (y) using machinery K (mea- sured...

 

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Consider the firm Plainview Oil, which produces barrels of oil (y) using machinery K (mea- sured in machine-hours) and workers L (measured in person-hours). Plainview Oil's tech- nology is represented by the production function y(L, K) = 2 min{L,3K}. Let r be the cost of one machine-hour and let w be the wage rate (i.e. the cost of one person-hour). (a) What kind of returns to scale does Plainview Oil's production exhibit? Justify your answer mathematically. (b) Draw the iso-quant curve corresponding to output of 15 units, with L on the horizontal axis and K on the vertical axis. Label any points where the slope of the iso-quant curve changes. (c) Suppose that the costs of inputs are r = 6 and w = 4. Determine Plainview Oil's cost function, c(y). (d) Derive Plainview Oil's average cost curve, AC(y), and marginal cost curve, MC(y). (e) On a graph that has costs on the vertical axis and output quantity y on the horizontal axis, plot the firm's cost curve, c(y); average cost curve, AC(y); and marginal cost curve, MC(y). Label the slope of each curve. Consider the firm Plainview Oil, which produces barrels of oil (y) using machinery K (mea- sured in machine-hours) and workers L (measured in person-hours). Plainview Oil's tech- nology is represented by the production function y(L, K) = 2 min{L,3K}. Let r be the cost of one machine-hour and let w be the wage rate (i.e. the cost of one person-hour). (a) What kind of returns to scale does Plainview Oil's production exhibit? Justify your answer mathematically. (b) Draw the iso-quant curve corresponding to output of 15 units, with L on the horizontal axis and K on the vertical axis. Label any points where the slope of the iso-quant curve changes. (c) Suppose that the costs of inputs are r = 6 and w = 4. Determine Plainview Oil's cost function, c(y). (d) Derive Plainview Oil's average cost curve, AC(y), and marginal cost curve, MC(y). (e) On a graph that has costs on the vertical axis and output quantity y on the horizontal axis, plot the firm's cost curve, c(y); average cost curve, AC(y); and marginal cost curve, MC(y). Label the slope of each curve.

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