the economies of scale curve in Figure 1.4 can be represented algebraically in t
ID: 2426700 • Letter: T
Question
the economies of scale curve in Figure 1.4 can be represented algebraically in the following equation:
Average costs= a + bQ + cQ2
where Q is the quantity produced by a firm and a, b, and c are coefficients that are estimated from industry data. For example, it has been shown that the economies of scale curve for U.S. savings and loans is:
Average Costs= 2.38 - .615A + .54A2
where A is a savings and loan's total assets. QUESTION: Using this equation, what is the optimal size of a savings and loan? (Hint: Plug in different values of A and calculate average costs. The lowest possible average cost is the optimal size for a savings and loan.)
Explanation / Answer
Average cost Function=C=2.38-0.615A+0.54A^2 Total cost = A*Avg cost TC=2.38A-0.615A^2+0.54*a^3 Derivative of total cost with A d[TC]/d A= 2.38-1.23A+1.62*A^2 when the cost is min d[minC}/dA= 3.24*A-1.23=0 A=0.38 So optimal value of A=0.38
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