A monopolist faces a demand curve Q = -0.5P + 500, and has a total cost function . TC(yf)=3y^2f+40000

a) Find the profit maximizing price, quantity and profit. Draw a picture showing the producer and consumer surplus in this market. Calculate the monopoly burden (dead weight loss).

Suppose the government, knowing that monopolies make consumers worse off, and can sustain economic profits, sets out to do something.

b) Assume initially that the government charges the monopoly a tax of 10,000 so that the new cost function is TC(yf)=3y^2f+50000 and that this tax money is given to the consumers. Show that this action

i) keeps the excess burden the same size,

ii)} eliminates the firm's profit.

c) Now assume the government issues a 100 per unit tax on the firm. This changes the cost function to TC(yf)=3y^2f+100yf+40000, and the tax money is given to the consumers. Show that this action

i) increases excess burden, . (Note: When calculating monopoly burden, you must use the orgininal MC, not the one with the tax in it.)

ii) leaves firms with positive profits,

iii) makes consumers worse off than the tax in (b) if consumer well-being is measured by cosumer surplus + tax revenue.