Question

Assume that a rural healthcare market is dominated by one seller (monopoly). If the marginal cost to the firm is

MC= 8+3Q

and the demand curve and marginal revenue curves are given by

Demand: P = 20 - 4.5Q

MR: P= 20 - 9Q

If the government attempts to correct the market failure by setting the price equal to $11, is the government failure or the market failure bigger? Show your work.

Answer 1

When the monopoly is working, the optimal rule of MR = MC gives a profit maximizing combination of P and Q where 20 - 9Q = 8 + 3Q or 12Q = 12. This gives Q = 1 and P = 20 - 4.5*1 = $15.5. Market failure is measured by deadweight loss which is the area of region ABD = 0.5*(15.5 - 11)*1.6 = $3.6

When government sets a price of $11, it is able to sell 2 units and the resultant deadweight loss is area of the region BDC = 0.5*(2 - 1)*(12.8 - 11) = $0.9

Hence market failure is bigger than the government failure