Question

Background: A State Environmental Regulatory Agency is thinking about establishing a program to reduce pesticide use on farms by subsidizing farmers in the State to produce less agricultural crops. The expressed goal of the program is to lower total pesticide levels in the water bodies of the State. The Agency is given the following information about the individual farms that would produce agricultural commodities in the State. Each farm sells its crops (q) in a perfectly competitive market. The price of each farm’s output is given by P. The costs of producing agricultural commodities by each farm is given by C(q). Each farm’s marginal costs increase at an increasing rate as they produce more crops, in other words, C′ \succ0, C" \succ0. For purposes here we assume that each farm receives a subsidy for selecting a level of crop production that is below from fixed output (i.e., crop) level set by a regulator, whose goal is to achieve lower concentrations of pesticides in the State’s water bodies. Let the subsidy equal S = α (q-bar-q) where α = βD' represents the marginal social costs (i.e., the damages caused by the pesticides that the farms are emitting) of producing q, and β is an emissions coefficient linking pesticides to the amount of output the farms produce; q-bar in this case represents the output that the farm would produce in the marketplace in the absence of the any policy on subsidies to reduce pollution if q = q-bar, the producer receives no subsidy, S = 0

1. Given profit-maximization as the goal for a typical farm, how would marginal costs of producing output change with the subsidy program for a representative farm? How would a representative farm’s average costs change with the subsidy program? Explain what effect the subsidy would have on the representative farm’s marginal and average costs and its supply curve in the short run.

Answer 1

Marginal Cost, Average costs and Optimal Subsidies

The optimal subsidy can be defined as that which will maximize social welfare, and social welfare can be calculated as total revenues minus total cost plus consumer surplus. From this, it can be shown that social welfare is maximized when prices equal marginal cost (Elgar and Kennedy 2005). When the price is reduced from P0 to P1, which is equal to marginal cost, then total welfare increases,

When marginal cost is less than average cost, then average cost decreases with increases in output. Conversely, when marginal cost is greater than average cost, then average cost will increase with output. A production process with the cost curves depicted in Figure 2 experiences increasing returns to scale up to the Q1 level of output and decreasing returns to scale with output greater than Q1. If the individual farms have has increasing returns to scale, then marginal cost is lower than average cost. The farmers would need to set prices equal to average total cost for it to cover all of its costs, but doing so would result in a decrease in consumer surplus and total social welfare. Setting price equal to marginal cost, therefore, would require a subsidy. The subsidy is required to maintain optimal allocation of resources and efficient levels of production.