Exam 19: Cost Minimization-Part A

A new metal alloy is discovered that uses copper and zinc in fixed proportions where each unit of the alloy requires 2 units of zinc and 2 units of copper.If no other inputs are required, if the price of zinc is $3 per unit, and the price of copper is $3 per unit and if total output is 5,000 units, what is the average cost per unit of output?

Al's production function for deer is f(x1, x2)= (2x₁ + x₂)^1/2, 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 7 deer is

The total cost function c(w1, w2, y)expresses the cost per unit of output as a function of input prices and output.

As assistant vice president in charge of production for a computer firm, you are asked to calculate the cost of producing 170 computers.The production function is q = min{x, y} where x and y are the amounts of two factors used.The price of x is $18 and the price of y is $10.What is your answer?

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 $8,000 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?

If output is produced according to Q =4L +6K, the price of K is $24, and the price of L is $20, then the cost-minimizing combination of K and L capable of producing 72 units of output is

The Chrysler Belvedere Truck Plant is attempting to minimize production costs.Over one month, 3,200 fenders are needed on the production line, which runs continuously.If it costs $400 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?

If there are increasing returns to scale, then costs per unit of output decrease as you move downward and to the right along an isocost line.

A lobbyist in our nation's capitol must buy 250 votes in the House of Representatives and Senate to win passage of a bill to add Millard Fillmore's face to Mount Rushmore.Votes in Congress can be purchased according to the following process: V =CM/100,000, where C is the number of dollars contributed to campaign funds and M is the number of three-martini lunches.If three-martini lunches cost $64 each, what is the smallest expenditure the lobbyist could make to ensure Mr.Fillmore's proper place in history?

A lobbyist in our nation's capitol must buy 250 votes in the House of Representatives and Senate to win passage of a bill to add Millard Fillmore's face to Mount Rushmore.Votes in Congress can be purchased according to the following process: V = CM/100,000, where C is the number of dollars contributed to campaign funds and M is the number of three-martini lunches.If three-martini lunches cost $25 each, what is the smallest expenditure the lobbyist could make to ensure Mr.Fillmore's proper place in history?

An orange grower has discovered a process for producing oranges that requires two inputs.The production function is Q =min{2x1, x2}, where x1 and x2 are the amounts of inputs 1 and 2 that he uses.The prices of these two inputs are w1 =$5 and w2 = $10, respectively.The minimum cost of producing 160 units is therefore

A new metal alloy is discovered that uses copper and zinc in fixed proportions where each unit of the alloy requires 4 units of zinc and 2 units of copper.If no other inputs are required, if the price of zinc is $2 per unit, and the price of copper is $5 per unit and if total output is 4,000 units, what is the average cost per unit of output?

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 $9 per unit.Each company produces 90 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?

The cost function c(w1, w2, y)expresses the cost per unit of output of producing y units of output if equal amounts of both factors are used.

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 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.

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 with the production function f (x1, x2, x3, x4)= min{x1, x2, x3, x4} faces input prices w1 = $1, w2 = $2,w3 = $2, w4= $5 for factors 1, 2, 3, and 4.The firm must use at least 17 units of factor 2.The lowest cost at which it can produce 100 units of output is