The demand for a monopolist’s product is: P = 40 -2Q; the monopolist’s total cost function...

The demand for a monopolist’s product is: P = 40 -2Q; the monopolist’s total cost function is: TC = 8Q + 0.5Q^2.(a)Under free monopoly, what is the numerical value of the dead-weight loss (DWL)? (b) Compute the monopolist’s break-even points and graph in the same diagram, demand (D), marginal revenue (MR), marginal cost (MC) and average cost (AC); in diagrams directly below, graph total revenue (TR), total cost (TC) and profit (pi).(c) Under short-run regulation, what are the market gains?

Solutions

Expert Solution

(a)Under free monopoly, MR is 40 - 4Q and MC is 8 + Q. This gives MR = MC or 40 - 4Q = 8 + Q. Now Q = (40 - 8)/5 = 6.4 units and price P = 27.2 per unit. DWL = 0.5*(monopoly price - MR at monopoly quantity)*(competitive quantity - monopoly quantity) = 0.5*(27.2 - 14.4)*(10.66 - 6.4) = 27.264

(b) Break even occurs where TR = TC or P = ATC. Here ATC is 8 + 0.5Q. Note that when Q = 0, TR = TC = 0. This is the first break even point. Also

40 - 2Q = 8 + 0.5Q

Q = 32/2.5 = 12.8 and P = ATC = 14.4. This the second break even point.

(c) Under short-run regulation, Price can be equal to AC when there are no economic profits. If price is set equal to MC, then we have Q = 10.66, P = 18.66 and AC = 13.33. This gives a profit of 56.88

Rahul Sunny answered 1 year ago

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