Exam 31: Production

Robinson Crusoe spends 4 hours a day catching fish and picking coconuts. He can always catch 2 fish per hour and he can always gather 3 coconuts per hour. His utility function is CF, where C is the number of coconuts he eats per day and F is the number of fish he eats per day. How many fish will he choose to eat per day?

Every consumer has a red-money income and a blue-money income and each commodity has a red price and a blue price. You can buy a good by paying for it either with blue money at the blue price or with red money at the red price. Harold has 7 units of red money to spend and 32 units of blue money to spend. The red price of ambrosia is 1 and the blue price of ambrosia is 4. The red price of bubble gum is 1 and the blue price of bubble gum is 2. If ambrosia is on the horizontal axis, and bubble gum on the vertical axis, then Harold's budget set is bounded by

For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is smelted. The cost of mining and processing 1 carload of ore is C(Q) = 400 + 2Q + 0.04Q². The demand for silver (per ounce) is P_s = 30 - 0.30Q_s and the demand for lead (per pound) is P_l = 6 - 0.02Q_l. What should the owners of the Matchless Mine do to maximize profits (in the long run)?

On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There are 1,000 acres of land. An acre of land will produce either 3 units of milk or 32 units of wheat. Some citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions of the form U(M, W) = MW. At every Pareto optimal allocation,

On a certain small island, there are 100 units of labor and 200 units of capital. Two goods can be produced. Good A is produced with fixed coefficients, using 1 unit of labor and 3 units of capital per unit of output. Good B is produced with fixed coefficients, using 1 unit of labor and 1 unit of capital per unit of output. Let X a denote the quantity of good A and X b be the quantity of good B that is produced. The set of feasible output combinations for this economy is restricted by the fact that it cannot use more than 100 units of labor or 200 units of capital. a. Write down two inequalities expressed in terms of X a and X b that must be satisfied at feasible output combinations. b. Draw a graph showing the economy's production possibility set. Put numerical labels on your graph so that this graph is precisely described.

If there are constant returns to scale in an industry, then in competitive equilibrium, profits in that industry must necessarily be zero.

When there is production, a competitive equilibrium is not Pareto optimal unless there are increasing returns to scale.

Robinson Crusoe has exactly 8 hours per day to spend gathering coconuts or catching fish. He can catch 3 fish per hour or he can pick 6 coconuts per hour. His utility function is U(F, C) = FC, where F is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best possible way between catching fish and picking coconuts, his consumption will be the same as it would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1.

Every consumer has a red-money income and a blue-money income and each commodity has a red price and a blue price. You can buy a good by paying for it either with blue money at the blue price or with red money at the red price. Harold has 12 units of red money to spend and 40 units of blue money to spend. The red price of ambrosia is 1 and the blue price of ambrosia is 4. The red price of bubble gum is 1 and the blue price of bubble gum is 2. If ambrosia is on the horizontal axis, and bubble gum on the vertical axis, then Harold's budget set is bounded by

Mandy is a master wood-carver and Jerry is her apprentice. They will each work the same number of hours making toy cars. Each car requires 4 wheels and 1 body. Mandy makes wheels at the rate of 25 per hour and bodies at the rate of 10 per hour. Jerry makes wheels at the rate of 10 per hour and bodies at the rate of 10 per hour. If they wish to maximize output, how many wheels should Jerry make per hour?

Robinson Crusoe has exactly 10 hours per day to spend gathering coconuts or catching fish. He can catch 3 fish per hour or he can pick 6 coconuts per hour. His utility function is U(F, C) = FC, where F is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best possible way between catching fish and picking coconuts, his consumption will be the same as it would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1.

The marginal rate of transformation between two goods indicates the rate at which an efficient economy would have to give up one good to obtain more of the other.

Last year a pestilential fungus ravaged the cocoa fields. The price of chocolate has risen abruptly to $1 per ounce. The government is considering emergency measures to aid suffering chocolate addicts. One plan being considered is the Chocolate Relief Plan (CRP). This plan would set a price ceiling of $.80 per ounce on chocolate. This would cause a shortage, so the CRP will limit consumption to no more than 10 ounces of chocolate per person per week. At $.80 per ounce, enough chocolate would be produced for everyone to have 10 ounces. Jill buys less than 10 ounces per week at $1 per ounce but would buy more than 10 ounces if the price dropped to $.80.

In the process of producing 1 hormone-free, stress-free, happy cow, the New Age Cattle Ranch produces 1 ton of natural, organic plant fertilizer. Demand for the ranch's cattle is given by P_c = 2,000 - 20Q_c, and demand for fertilizer is given by P_f = 500 - 4Q_f. The cost of producing Q cow-fertilizer bundles is C = 5,000 + 400Q. To maximize profits, the ranch should

Every consumer has a red-money income and a blue-money income and each commodity has a red price and a blue price. You can buy a good by paying for it either with blue money at the blue price or with red money at the red price. Harold has 40 units of red money to spend and 35 units of blue money to spend. The red price of ambrosia is 4 and the blue price of ambrosia is 5. The red price of bubble gum is 1 and the blue price of bubble gum is 1. If ambrosia is on the horizontal axis, and bubble gum on the vertical axis, then Harold's budget set is bounded by

A small company produces two goods, swords and plowshares. The company has 100 type alpha employees and 100 type beta employees. If an alpha devotes all his time to producing swords, he can make 4 swords per week. If he devotes all his time to producing plowshares, he can make 20 plowshares per week. A beta can produce either 1 plowshare per week or 1 sword per week. The company wants to produce 413 swords and as many plowshares as it can. How many type betas should it employ at making swords?

Robinson Crusoe has exactly 14 hours per day to spend gathering coconuts or catching fish. He can catch 4 fish per hour or he can pick 12 coconuts per hour. His utility function is U(F, C) = FC, where F is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best possible way between catching fish and picking coconuts, his consumption will be the same as it would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1.

There are two people and two goods, person A has comparative advantage in the production of good 1 if and only if it takes person A less time to produce good 1 than it takes person B.

Tip can write 3 pages of term paper or solve 9 workbook problems in an hour, while Spot can write 4 pages of term paper or solve 4 workbook problems in an hour. If they each decide to work a total of 7 hours and to share their output, then if they produce as many pages of term paper as possible given that they produce 18 workbook problems,

For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is smelted. The cost of mining and processing 1 carload of ore is C(Q) = 300 + 3Q + 0.02Q². The demand for silver (per ounce) is P_s = 30 - 0.10Q_s and the demand for lead (per pound) is P_l = 6 - 0.03Q_l. What should the owners of the Matchless Mine do to maximize profits (in the long run)?