Exercise 4

Due Monday 2/21

When pollution control regulations are first established (or when they are substantially tightened) existing plants are often given special, more lenient rules or exempted from the regulations entirely. This is known as “grandfathering” and it is very controversial, at least in retrospect. In some states, factories that were grandfathered decades ago remain exempt from essentially all air pollution regulations.

This problem asks you to analyze grandfathering by working through a stylized example. Suppose there are 1 million households that consume a particular product. Each household’s demand for the good is given by P = 100 – 4*Qi, where Qi is the amount of the good household i consumes. The product is produced by 100 identical, perfectly-competitive firms, each of which has a marginal cost of $20 and a maximum capacity of 200,000 units. (The capacity constraint means that each firm's marginal cost curve is shaped like a backward L: horizontal at $20 up to 200K units and then vertical at that point. It's as though the cost of producing beyond 200K units is nearly infinite.) In addition, production of the good creates pollution that causes $4 worth of damage per unit produced.

1. Solve for the market equilibrium. Determine the price, total quantity, quantity purchased by each household, and the quantity produced by each firm. Is this efficient? If not, please calculate the following things: the efficient price, the efficient total output, and the social surplus that could be gained by moving from the market equilibrium to the efficient point.
2. Over time, the population in the region is expected to grow to 2 million. Suppose that the government passes a law requiring new firms in the industry to use a pollution control device that eliminates their pollution but raises their marginal cost to $24 per unit. The existing 100 firms are exempt as long as they do not increase their capacity beyond 200,000 units. Determine the market equilibrium price and total quantity after the population increase. How much of the total output will be produced by new firms entering the market? How much by the old firms?
3. Are the old firms better or worse off than they were in part (1)? Calculate how much each of the old firms gains or loses each year relative to part (1). What is the present value of this stream one year before it begins? Discuss the implications of this for the political process. You may assume the interest rate is 5%.