The Poster Bed Company believes that its industry can best be classified as monopolistically competitive. An analysis of the demand for its canopy bed has resulted in the following estimated demand function (P), inverse demand function (Q), total revenue function (TR), and marginal revenue function (MR): (6 points)
P = 910 - 6Q è Q = 151.67 - .167P
TR = 910Q -6Q2
MR = 910 - 12Q
The cost analysis department has estimated the total cost function (TC) and the marginal cost function (MC) for the poster bed as:
TC = 30Q2 + 10Q + 2000
MC = 60Q + 10
a) Calculate the level of output that should be produced to maximize short run profits.
(Hint: Set MR = MC and solve for Q)
b) What price should be charged?
c) Compute total profit at this price - output combination.
d) Compute the point price elasticity of demand at the profit-maximizing level of output.