Hawkins MicroBrewery has a monopoly on Oatmeal Stout in the

Hawkins MicroBrewery has a monopoly on Oatmeal Stout in the local market. The demand is:  QD = 100 - 2P ? P = 50 –(1/2)Q.   The resulting marginal revenue function is MR(Q) = 50 - Q. Hawkins marginal cost of producing Oatmeal Stout is MC(Q) = 5 + (1/2)Q and total cost equals 5Q+(Q^2)/4.  

a. Calculate Hawkins profit maximizing output as well as profits.

Solution

ANS:

a.) Hawkins will set marginal revenue equal to marginal cost to find optimal output.

MR(Q) = 50 - Q = MC(Q) = 5 + 1 2 Q Q = 30.  

At this output level, Hawkins charges $35 per unit.  The choke price is $50 while Hawkins reservation price is $5.  Consumer surplus is:

CS = 1 2 (50 - 35)30 = 225.

Producer surplus is  PS = 0.5(20 - 15)(30) + (35 - 20)(30) = 675.

Total surplus in the local Oatmeal Stout market is $900 when Hawkins has monopoly power.  If Hawkins did not have monopoly power, the price of Oatmeal Stout would equal Hawkins marginal cost.  We can find this output level by setting consumers price as a function of output equal to Hawkins marginal cost.

P = 50 - 1 2 Q = MC = 5 + 1 2 Q Q = 45. At this output level, the price of Oatmeal Stout is $27.50.

Consumer surplus is CS = 1 2 (50 - 27.50)45 = 506.25. Producer surplus is PS = 1 2 (27.50 - 5)45 = 506.25.

Total surplus when Hawkins does not have monopoly power would be $1,012.50.

b.) Thus, society loses 112.50 of surplus due to Hawkins monopoly power in the local Oatmeal Stout market.