Exam 19: Cost Minimization

A firm's production function is q = 26x0.33y0.67, 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 6 times the price of factor y,the ratio in which the firm will use factors x and y is closest to

A firm has fixed costs of $2,000. Its short-run production function is y = 4 , where x is the amount of variable factor it uses. The price of the variable factor is $3,000 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 $640,000 and if its chances of winning a case are , 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?

The production function is f (L, M) = 4 , where L is the number of units of labor and M is the number of machines used. If the cost of labor is $36 per unit and the cost of machines is $4 per unit, then the total cost of producing 6 units of output will be

Al's production function for deer is f (x1, x2) = , where x1 is the amount of plastic and x2 is the amount of wood used. If the cost of plastic is $6 per unit and the cost of wood is $1 per unit, then the cost of producing 5 deer is

A firm uses a single variable input x to produce outputs according to the production function f (x) = 300x 6x2. This firm has fixed costs of $300. This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.

If output is produced according to Q = 4LK, the price of K is $10, and the price of L is $40, then the cost minimizing cost minimizing combination of K and L capable of producing 64 units of output is

The Chrysler Belvedere Truck Plant is attempting to minimize production costs. Over one month, 1,600 fenders are needed on the production line, which runs continuously. If it costs $200 to set up the stamping press to produce fenders and $1 per month to store produced fenders, how many times should the stamping press be run per month?

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?

Quasi-fixed costs are those costs that can be avoided if and only if a firm produces zero output.

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 360 bagels a week to be sold continuously?

A firm produces Ping-Pong balls using two inputs. When input prices are ($15, $7) the firm uses the input bundle (17, 71). When the input prices are ($12, $24) the firm uses the bundle (77, 4). The amount of output is the same in both cases. Is this behavior consistent with WACM?

A firm has production function f (x1, x2, x3, x4) =min{x1, x2} + min{x3, x4}. This firm faces competitive factor markets where the prices for the four factors are w1 = $4, w2 = $8, w3 = $5, and w4 = $3. The firm must use at least 20 units of factor 2. The cost of producing 100 units in the cheapest possible way 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 , 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?

Vincent Smudge, an avant-garde New York artist,creates "living sculpture" by smearing paint slowly all over himself. S hours of "living sculpture" can be created by S = min{L, }, where L is hours of labor by Mr. Smudge and T is tubes of water-soluble paint.Since Mr. Smudge is a highly renowned artist, his labor costs $50 per hour, while paint costs $10 per tube.Using a $3,000 grant from the National endowment for the Arts, how many hours of "living sculpture" can Mr.Smudge create?

A firm has a production function described as follows:"Weekly output is equal to the square root of the minimum of the amount of capital and the number of hours of labor used per week." Suppose that the cost of a unit of capital is r and the price of a unit of labor is w and the level of output is y. Write down the long-run total cost as a function of w, r, and y.

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

A competitive, cost-minimizing firm has the production function f (x, y) = x + 2y and uses positive amounts of both inputs. If the price of x doubles and the price of y triples, then the cost of production will more than double.

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 = 2P + 5C, where P is pounds of plastic and C is pounds of clay. Plastic costs $5 per pound and clay costs $2 per pound. What would be the lowest cost of producing 60,000 figurines?

A firm uses a single variable input x to produce outputs according to the production function f (x) = 300x 6x2. This firm has fixed costs of $400. This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.