Answer to Question #285162 in Microeconomics for bluesea349

Question

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. 

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.