Answer to Question #88181 in Microeconomics for Kanaha

Question

A bicycle manufacture faces a horizontal demand curve . the firm's total cost are given by the equation . TVC = 150Q - 20Q2 + Q3 where Q is the quantity. Below what price should the firm shut down opera

Answer 1

The firm should shut down operation if price falls below $50.

Explanation

The shut-down point of a company is a point whereby the marginal cost (MC) of a firm is equal to the average variable cost (AVC). At this point, the firm will gain more by shutting down temporarily instead of continuing being in business.

Marginal cost of a firm is a derivative of the total cost with respect to the quantity. Therefore;

MC=dTVC/dQ

     =150Q - 20Q2 + Q3/Q

   =150 -40Q +3Q²

According to profit maximization theory, P=MC, thus P= 150 -40Q +3Q²

Average variable equation is given by;

AVC = TVC/Q

         =150Q – 20Q² +Q³) / Q

        = 150 -20Q +Q²

The next step is to equate the two equations, that is MC and AVC

MC=AVC

  150 -40Q +3Q² =150 -20Q +Q²

2Q2-20Q or

2Q (Q-10) =0

Thus, Q = 0 and Q = 10

The next step is to substitute Q=10 in the marginal cost equation

=150 -40Q +3Q²

=150-40(10) +3(100)

=150-400+300

=50

Therefore, P=$50.

Similarly, substitute Q=0 in the marginal equation

= 150 -40Q +3Q²

=150-40(0) +0

=150

Therefore, P=$150.

A firm will shut down operations when P < AVC

Thus, in this case the firm will shut down when the price falls below $50.

Reference

Krugman, P. R., Wells, R., Ray, M., & Anderson, D. A. (2011). Microeconomics. New York, NY: Worth.