Consider an industry in which there are a large number of potential firms. Each
ID: 1250309 • Letter: C
Question
Consider an industry in which there are a large number of potential firms. Each firm in theindustry has the same production process and produces output using capital and labor. Assume that
capital and labor both exhibit diminishing marginal returns, so that capital can be substituted for labor in
the production process (and vice versa), but capital and labor are not perfect substitutes.
Assume further that each firm is too small to affect the market wage rate for labor and that each firm is
too small to affect the market rental rate on capital. Finally, assume that when the firm uses capital, it
discharges pollutants into the local river.
Because the town’s drinking water comes from the local river, the townspeople are concerned about
water quality and ask the town council to force the firms to discharge less pollution into the local river.
One councilman responds by proposing a tax per unit of pollution that is discharged into the river.
Another councilman suggests that – instead of imposing a tax on pollution discharges – the town should offer firms a subsidy per unit of pollution that they do not discharge into the river.
5. Suppose that each firm in the industry minimizes the cost of producing a given level of output.
· How would such a subsidy affect the relative wage rate? Explain.
· How would such a subsidy affect the optimal combination of capital and labor that
each firm uses to produce output? Explain.
· Illustrate your answer to the previous question with isoquants and isocosts.
Explanation / Answer
You have to think of this in a kind of weird way. Subsidies are always equivalent to taxes. In this case, it's as if the town were giving firms a big wad of cash if they were to use zero capital. For each unit of capital that they use, the cash is reduced. It's implicitly a tax on using capital. There's this extra cost of using capital -- the lost subsidy. Once more, this causes capital to become more expensive relative to labor, so the relative wage decreases. The income and scale effects are just the same as with a tax: capital use goes down, while labor depends on which effect dominates. The shape of the isoquant curves stays the same, and isocost curves pivot in exactly the same way that they did with the tax.