A monopolistically competitive firm has an average total cost curve given by ATC = 2/Q+ 1+Q/8. The slope of this curve is given by 1/8-2/Q2 . The marginal cost is MC = 1+Q/4. Her demand curve is given by P = 3-(3/8)Q, and so the marginal revenue curve is given by MR = 3-(3/4)Q. We know that the equilibrium for this firm (see Figure 11.2) is where the demand curve is tangent to the ATC curve - where the slopes are equal.
(a) What is the equilibrium output for this firm [Hint: find where the slope of the demand curve equals the slope of the ATC curve]?
(b) At what price will the producer sell this output?
(c) Solve for where MC = MR, this is the profit maximizing condition - does it correspond to where the slope of the demand curve equals the slope of the ATC?
(d) Since the MC always intersects the ATC at the minimum of the ATC, solve for the output level that defines this ATC minimum.
Figure 11.2
