Question

Surrounding the Great Lake are four paper-mills, each producing 100 tons of paper per year. The paper is sold on the national market for $2 per ton, and including all the costs of production, costs for each firm are $1 per ton. Thus each firm earns a pure economic profit of $1 per ton. These paper mills require fresh water to operate, and also produce a pollutant called gunk, which they dump into the Great Lake.

New paper mills can also locate on the Great Lake, and produce at a base cost of $1 per ton. However, for each new paper mill which arrives, the water will become more polluted with gunk, and each firm will have to install a water treatment facility to obtain fresh water. This externality associated with new plants will raise the costs of paper production at all facilities, including the new one, by $.15 per ton for each new mill.

1. Draw a diagram of the marginal cost and marginal revenue curves with the number of mills on the horizontal axis. Assume that government regulation restricts lake access to the profit-maximizing number of firms. Show the resource rent that would be earned by the mills which are allowed to operate.
2. Suppose that government regulation reduced the number of mills by one from the number that would have resulted given free access. Show that the increase in profits to the remaining firms (the resource rent) is sufficient to compensate the firm that is denied access for its lost profits.

Answer 1

Given free access, 6 new miles will locate on great lakes, for a total of 10. Revenue for 10 mile is $200, while private costs will be $190, which creates profit for each firm, including 10^th of $5. The 11^th mill will lose money.

The total profit maximizing number of mills = 5

The entry of 5^th plant will causes total costs at all plants to increase by $175, but revenues go up by $200. The 6^th plant increases industry-wide cost by $205 against revenue of only $200. This industry profits fall as entry proceeds beyond five plants.

Total profits at 4th plants = 4(200-100) = $400

Total profits at 5^th p;ant = 5(200-115) = $425

At 6^th plant = 6(200-130)= $420

At 7^th plant = 7(200-145)= $385.

d. loss profit = $200-$190 = $10

increased profit = 9)$15 = $135

net increase in profits = $135-$10=$125

the government restricts access to lake 9 plants in total. Show that the increase in profits to the 9 firms is more than the lost profit to the 10^th firm which is denied access.