Answer to Question #285170 in Microeconomics for Khaled

Question

7. You are given the following long-run cost function:

TC = 160Q - 20Q2 + 1.2Q3

a. Calculate the long-run average cost and marginal cost. Plot these costs on a graph.

b. Describe the nature of this function’s scale economies. Over what range of output does economies of scale exist? Diseconomies of scale? Show this on the graph.

Refer to Appendix 7B for help in answering Problems 8 and 9.

Answer 1

Solution:

a.). Long-run average cost = Total long-run cost/Quantity

= 160Q - 20Q² + 1.2Q³ $\div$ Q = 160 – 20Q + 1/2Q²

Long-run average cost = 160 – 20Q + 1/2Q²

 

Long-run Marginal cost = $\frac{\partial LTC} {\partial Q}$ = 160 – 40Q + 3.6Q²

Long-run Marginal cost = 160 – 40Q + 3.6Q²

 

The graph showing the LRAC and LMC is as below:

b.). Economies of scale exist when output is low and diseconomies of scale exist when the quantity increases as depicted on the graph.