Question

Welfare analysis can get complicated if there are multiple market failures. “The General Theory of the Second Best,” by Lipsey and Lancaster (Review of Economic Studies 24 (1956–57): 11–32) argues that when there are multiple market failures, fixing only one market failure may make things worse than doing nothing. Two market failures may work in opposite directions; for instance, fixing one may have unintended consequences for the other. For example, consider a monopolist that pollutes. When a firm is a monopolist, it reduces its production so that it can increase price; although it sells fewer units, the higher price more than makes up for the reduced volume. Consumers lose, and total welfare is reduced, due to the higher price and lower quantity. The pollution problem, in contrast, is excess production.

a. Draw a supply-demand figure for a firm with the demand curve Q = 10 - P, and marginal cost curve MC = 2 (based on total costs C = 2 * Q). If this were not a monopoly, what would be the equilibrium price and quantity? Calculate the firm’s total revenue, total cost, and profit. Also calculate consumer surplus. Net benefits are consumer surplus plus producer surplus, which equals profit in this case; calculate that value.

b. Suppose that, instead, the firm decided to act like a monopolist and restrict output. It produces 4 units and charges $6 for each unit. Calculate the firm’s total revenue, total cost, and profit; consumer surplus; and net benefits. Are net benefits higher or lower? Is the firm better or worse off?

c. Now let’s consider the pollution problem. Suppose the firm produces marginal damages of $4/unit. For (a) and (b), recalculate net benefits to account for the social damages.

d. Find the new efficient equilibrium, now that social marginal costs are $6/unit. Calculate the firm’s total revenue, total cost (including the pollution cost), and profit; consumer surplus; and net benefits.

e. The monopolist, if forced to pay social marginal costs, will produce 2  units and charge $8 for each unit. Calculate the firm’s total revenue, total cost (including the pollution cost), and profit; consumer surplus; and net benefits.

f.Compare the results for (c), (d), and (e). Rank them from the highest net benefits to the lowest.

g. A regulator who can break up monopolies is examining this situation. Compare net benefits for the monopolist who pollutes [the recalculation for the monopolist in Part (c)] with the competitive firm that pollutes [the recalculation for the competitive firm in Part (c)]. Will the regulator improve net benefits by breaking up the monopoly?

h. A regulator who addresses pollution separately examines the situation. Compare net benefits for the monopolist who pollutes [the recalculation for the monopolist in (c)] with net benefits for the monopolist who pays the full costs of pollution in (e). Will this regulator increase net benefits by taxing pollution?

i. Does the Theory of the Second Best apply here? Does fixing a market failure always improve welfare, compared to not fixing it?

Answer 1

So, let’s assume that the demand curve be, “Q = 10 – P” and the “MC=2”, => the equilibrium “P” and the quantity choice will be determined by the condition “P=MC=2”.

=> Q = 10 – P = 10 – 2 = 8, => the optimum “P=2” and the quantity production is “Q=8”.

So, here total revenue is “P*Q=2*8 = 16” and total cost is “2*Q = 2*8 = 16”, => the profit is the difference between “TR” and “TC”, => profit is “0”. Consider the following fig.

Now, the consumer surplus is the area above the price level under the demand curve.

=> CS = 0.5*(10-2)*8 = 0.5*8*8 = 32 and the PS is “0” since here the “MC” is constant.

So, here the net benefit is nothing but the CS, => the net benefit is “CS = 32”.

b).

Now, suppose the firm decided to act like a monopolist and produce “Q=4” and “P=6”, => TR = P*Q = 6*4 = 24 and TC = 2*Q = 2*4 = 8, = > profit = TR – TC = 24 – 8 = 16.

Now, CS = 0.5*(10-6)*4 = 0.5*4*4 = 8 and PS = (6-2)*4 = 4*4 = 16.

=> Net benefit is “CS + PS = 8 + 16 = 32”. Consider the following fig.

So, here we can see that “CS” has fallen and “PS” has increased but the net benefit remain same at “32”.

Now, as the profit of the firm increases, => the firm is better off under monopoly case.

c).

Now, assume that there is an pollution problem of “$4” per unit. So, in the 1^st case the total product and “net benefit” were “Q=8” and “32” respectively. So, now as the producer produces “Q=8”, => total damage is “4*8 = 32”, => the new net benefit is “32-32 = 0”. So, here the net benefit reduced to “0”. Consider the following fig.

Now, in the second case “Q=4”, => total damage is “4*4 = 16”. Now, the “net benefit” was “32”, => the new net benefit is “32 – 16 = 16 > 0”.

d).

Now, the demand curve be “Q = 10 – P” and “SMC = 6”, => at the equilibrium “P=SMC”.

=> Q= 10 – 6 = 4, => P = 6 and Q = 4.

So, here “TR” is “6*4 = 24” and the “TC” is “6*4 = 24”, => profit is “0” the difference between “TR” and “TC”. Now, the “CS” is given by, “0.5*4*(10-6) = 0.5*4*4 = 8” and the producer surplus is “0” as the “P” is equal to “SMC”. Consider the following fig.

Now, under the monopoly case the optimum “Q” will be determined by the condition “MR=SMC”, where “MR = 10 – 2*Q”. => MR = SMC = 10 – 2*Q = 6, => 2*Q = 4, => Q= 2. So, here “P=8” and “Q=2”.

So, here “TR” is “8*2 = 16” and “TC=6*2 = 12”, => profit is “4” the difference between “TR” and ”TC”. Now, the “CS” is “0.5*(10-8)*2 = 0.5*2*2=2” and the “PS” is “(8-6)*2 = 2*2 = 4”. So, net benefit is given by, “CS + PS = 2 + 4 = 6”.