Chapter 8: Production Costs: Where Less Is More cost-minimizing input combination for a specific quantity of output. If you determine the cost-minimizing input combination for every output level, you have the points comprising the total cost function. Thus, the total cost function is derived from production theory. Figure 8-3 illustrates a series of production isoquants and isocost curves. Because a production isoquant represents a fixed quantity of output, the cost of producing that quantity of output is minimized at the point where the isocost curve is tangent to the isoquant. For the production isoquant qa, production cost is minimized by employing Ka of capital and La of labor. (See Chapter 6 for a more detailed explanation.) This results in the cost level Ca. So, one point on your total cost curve corresponds to output qa and total cost Ca. (See Figure 8-1.) Other points on your total cost curve are derived through the remaining production isoquants and isocost curve combinations.
Figure 8-3: Production isoquants and total cost.
Your firm’s production isoquant is
where q is the quantity of output produced, K is the quantity of capital employed in machine-hours, N is the quantity of land employed in acres, and L is the quantity of labor employed in hours. Capital and land are both fixed inputs. The quantity of capital is fixed at 400 machine-hours, and the quantity of land is fixed at 625 acres. Your input prices are $50 per machine-hour of capital, $40 per acre of land, and $25 per hour for labor. To convert the production isoquant into a total cost equation, take the following steps:
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