Exam 19: Cost Minimization-Part A

The production function is f (L, M)= 4L^1/2M^1/2, where L is the number of units of labor and M is the number of machines used.If the cost of labor is $49 per unit and the cost of machines is $16 per unit, then the total cost of producing 5 units of output will be

A firm's production function is q = 12x0.50y0.50, where x and y are the amounts of factors x and y that the firm uses as inputs.If the firm is minimizing unit costs and if the price of factor x is 5 times the price of factor y,the ratio in which the firm will use factors x and y is closest to

Douffelberry juice is a mild intoxicant, prized for facilitating conversation among university administrators but not otherwise valued.The berry does not travel well,so it must be squeezed on the farm where it is grown.Baskets of berries, B, are produced using ounces of seeds, S, and hours of labor, L, according to a production function B = S^1/2L^1/2.Gallons of juice, J, are made from baskets of berries and hours of labor according to the production function J =min{B, L}.If seeds cost $16 per ounce and labor costs $1 per hour, what is the cost of producing each gallon of douffelberry juice?

A firm has fixed costs of $4,000.Its short-run production function is y = 4x^1/2, where x is the amount of variable factor it uses.The price of the variable factor is $4,000 per unit.Where y is the amount of output, the short-run total cost function is

The law firm of Dewey, Cheatham, and Howe specializes in accident injury claims.The firm charges its clients 25% of any damage award given.The only cost to the firm of producing an accident injury claim is the time spent by a junior partner working on the case.Junior partners are paid $100 per hour for this drudgery.If the firm is suing for damages of $250,000 and if its chances of winning a case are 1/25h, where h is the number of hours spent working on the case, then to maximize its profits, how many hours should it have the junior partner spend working on the case?

Two firms, Wickedly Efficient Widgets (WEW)and Wildly Nepotistic Widgets (WNW), both produce widgets, using the same production function y = K^1/2L^1/2, where K is the amount of labor used and L is the amount of capital used.Each company can hire labor at $1 per unit of labor and capital at $1 per unit.Each company produces 10 widgets per week.WEW chooses its input combinations to produce in the cheapest way possible.Although it produces the same output per week as WEW, WNW is required by its dotty CEO to use twice as much labor as WEW.How much higher are WNW's total costs per week than WEW's?

If the production function for tuna casseroles is min{x1,x2 }, where x1 is the amount of factor 1 and x2 is the amount of factor x2, find the cost function for tuna casseroles.

Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{5/4C, 5P}, where M, C, and P are pounds of manicotti, cheese, and pasta respectively.If cheese costs $3 per pound and pasta costs $4 per pound, how much would it cost to produce 20 pounds of manicotti in the cheapest way possible?

If there are increasing returns to scale, then average costs are a decreasing function of output.

Using existing plant and equipment, Priceless Moments Figurines can be manufactured using plastic, clay, or any combination of these materials.A figurine can be manufactured by F = 4P + 2C, where P is pounds of plastic and C is pounds of clay.Plastic costs $2 per pound and clay costs $5 per pound.What would be the lowest cost of producing 40,000 figurines?

A competitive firm with output y has a production function y = (2x₁ + x₂)^1/2, where x1 and x2 are inputs used in production.The firm produces the output minimizing cost.With input prices w1 and w2, which of the following is true?

Nadine has a production function 2x1 + x2.If the factor prices are $8 for factor 1 and $5 for factor 2, how much will it cost her to produce 70 units of output?

A competitive firm uses three factors of production.Its production function is f (x, y, z)= (x + y)^1/2 z ^1/2.Originally the factor prices were wx = $1, wy = $2, and wz =$3.The prices of factors x and z decreased to half of their previous levels, but the price of factor y stayed constant.The cost of production

A competitive firm has the three-factor production function f (x, y, z)= (x + y)^1/2 z ^1/2.The factor prices used to be wx = $1, wy = $2, and wz = $3.Suppose that the price of factor y doubled while the other two prices stayed the same.Then the cost of production

Douffelberry juice is a mild intoxicant, prized for facilitating conversation among university administrators but not otherwise valued.The berry does not travel well,so it must be squeezed on the farm where it is grown.Baskets of berries, B, are produced using ounces of seeds, S, and hours of labor, L, according to a production function B =S^1/2L^1/2.Gallons of juice, J, are made from baskets of berries and hours of labor according to the production function J =min{B, L}.If seeds cost $9 per ounce and labor costs $9 per hour, what is the cost of producing each gallon of douffelberry juice?

A company can rent one of two copying machines.The first costs $34 a month to rent and costs an additional 2 cents per copy to use.The second costs $107 a month to rent and an additional 1 cent per copy to use.How many copies would the company need to make per month in order for it to be worthwhile to rent the second machine?

If it costs $20 to set up and later clean a bagel press and bagels cost $1 per week per bagel to store, how many times should the bagel press be run each week to produce 1,000 bagels a week to be sold continuously?

A firm has two factories.One factory has the cost function c1(y1)= 2y21 + 90 and the other has the cost function c2(y2)= 6y22 +40.If the firm wishes to produce a total of 32 units as cheaply as possible, how many units will be produced in the second factory?

A politician facing reelection can win votes according to the following process: V = 500S^0.20M^0.60, where S is hours of making campaign speeches and M is the number of flyers mailed.Making speeches costs $10 per hour, mailing flyers costs $.50 per flyer, and $2,000 are available to spend on the campaign.Assuming the politician wants to maximize votes, how should the budget be allocated between speeches and mailing flyers?

The production function is f (L, M)=5L^1/2M^1/2, where L is the number of units of labor and M is the number of machines.If the amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then the total cost of producing 12 units of output is