3. A firm’s total cost curve is TC = 40Q – 10Q2 + Q3. a. What...
3. A firm’s total cost curve is TC = 40Q – 10Q2 + Q3.
a. What are the equations for Marginal Cost and Average Total Cost?
b. What is the minimum efficient scale?
c. Over what range of output does the production function exhibit economies of scale, and over what range does it exhibit diseconomies of scale?
Homework Answers
a) MC = derivative of TC with respect to Q = 40 - 20Q + 3Q^2
AC = C/Q = 40 - 10Q + Q^2
b) At MES, MC = AC. This gives 40 - 20Q + 3Q^2 = 40 - 10Q + Q^2
2Q^2 - 10Q = 0
Q = 5
Hence MES is 5 units at which AC is minimum at 40 - 10*5 + 5^2 = $15.
c) From 0 to 5 there are economies of scale because AC is falling and reaching a minimum. From 5 units onwards there are diseconomies of scale because AC is rising after reaching its minimum.
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