Stanley Ford makes mountains out of molehills. He can do this with almost no effort, so for the purposes of this problem, let us assume that molehills are the only input used in the production of mountains. Suppose mountains are produced at constant returns to scale and that it takes 50 molehills to make 1 mountain. The current market price of molehills is $8 each. A few years ago, Stan bought an"option" that permits him to buy up to 2,000 molehills at $4 each. His option contract explicitly says that he can buy fewer than 2,000 molehills if he wishes, but he can not resell the molehills that he buys under this contract. In order to get governmental permission to produce mountains from molehills, Stanley would have to pay $10,000 for a molehill-masher’s license.

a. The marginal cost of producing a mountain for Stanley is __ if he produces fewer than 20 mountains. The marginal cost of producing a mountain is if he produces more than 20 mountains.
b. If the price of mountains is $1,600, how many mountains will Stanley produce?
c. The government is considering raising the price of a molehill-masher’s license to $11,000. Stanley claims that if it does so he will have to go out of business. Is Stanley telling the truth? What is the highest
fee for a license that the government could charge without driving him out of business?

a. The marginal cost of producing a mountain for Stanley is $200 if he produces fewer than 20 mountains. The marginal cost of producing a mountain is $200 if he produces more than 20 mountains.

b. If the price of mountains is $1,600, how many mountains will Stanley produce?

All the mountains that he is able to produce until the marginal cost = $1,600. Currently the marginal cost for up to 40 mountains is $200, and beyond that point it is $400.

c. The government is considering raising the price of a molehill-masher’s license to $11,000. Stanley claims that if it does so he will have to go out of business. Is Stanley telling the truth?

Stanley is lying, since he only needs to sell 8 mountains to break even at $11,000. With the 8th mountain sold, his profit will be $200.

d. What is the highest fee for a license that the government could charge without driving him out of business?

Assuming that all the materials that Stanley could purchase are 2,000 molehills and that his maximum output is 40 mountains, then the maximum price the government could charge for the license fee is = 40 mountains x $1,400 (contribution margin) = $56,000

Explanation:

Stanley can produce 2,000 / 50 = 40 mountains with his "cheap" molehills.

Since Stanley can purchase the molehills at a discount, he uses 50 x $4 = $200 of materials per mountain

Stanley's marginal costs are:

1 mountain = $10,000 + $200 = $10,200
2 - 40 mountains = 50 x $4 = $200
41 mountains and more = 50 x $8 = $400

If the price per mountain is $1,600, then Stanley will keep producing them at full capacity since the marginal cost is much lower than that. He will produce mountains until the marginal cost = $1,600

the approximate break even point for Stanley with a license fee of $11,000:

= 11,000 / $1,400 = 7.86 ≈ 8 mountains

if he sells 7 mountains his profit = $12,800 - $11,000 - $1,600 = $200

Assuming that all the materials that Stanley could purchase are 2,000 molehills and that his maximum output is 40 mountains, then the maximum price the government could charge for the license fee is:

40 mountains x $1,400 (contribution margin) = $56,000