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Exam 21:Cost Minimization-Part A

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Question 1

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The production function for good y is y =max{10x1,4x2},where x1 and x2 are the amounts of factors 1 and 2.Find the cost function for good y.

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The cost function is...

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Question 2

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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

A) $1,000.
B) $400.
C) $317.
D) $615.
E) $300.

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Question 3

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If output is produced according to Q = 4LK,the price of K is $10,and the price of L is $5,then the cost minimizing combination of K and L capable of producing 2 units of output is

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

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.If the amounts of both factors can be varied and if the cost of labor is $64 per unit and the cost of using machines is $1 per machine,then the total cost of producing 20 units of output is

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?

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

If output is produced according to Q = 4L + 6K,the price of K is $12,and the price of L is $20,then the cost-minimizing combination of K and L capable of producing 96 units of output is

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 =$7,w2 = $8,w3 = $6,and w4 = $5.The firm must use at least 20 units of factor 2.The cost of producing 100 units in the cheapest possible way is

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

The editors at Snoozeweek,a news magazine,constantly alter the proportion of celebrity photographs and mundane news stories so as to maximize the number of copies sold.A statistical consultant has estimated sales to be S =1,000C 0.60N 0.60,where C is the number of celebrity photographs and N is column inches of news stories.If the editors only have $8,000 to spend on each edition with celebrity photos costing $200 each and news stories costing $10 per column inch,what should the editors do

Suppose that the production function is f (x1,x2) = (min{x1,2x2}) .5.

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?

Joe's Bar and Grill uses two inputs,beer and pretzels.When the price of beer was $10 a case and the price of pretzels was $20 a case,Joe used 1 case of beer and 2 cases of pretzels a day.When the price of beer was $20 a case and the price of pretzels was $10 a case,Joe used 2 cases of beer and 1 case of pretzels a day.Joe produced the same output in each of these circumstances.

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

If the production function is given by f (x1,x2,x3,x4) =min{x1,x2} + min{x3,x4} and the prices of inputs (x1,x2,x3,x4) are (2,1,5,3) ,the minimum cost of producing 1 unit of output is closest to

Rocco's Pasta Bar makes manicotti according to an old family recipe which states M =min{3/2C,3P},where M,C,and P are pounds of manicotti,cheese,and pasta respectively.If cheese costs $3 per pound and pasta costs $1 per pound,how much would it cost to produce 10 pounds of manicotti in the cheapest way possible?

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.

A firm has the production function Q =KL,where K is the amount of capital and L is the amount of labor it uses as inputs.The cost per unit of capital is a rental fee r and the cost per unit of labor is a wage w.The conditional labor demand function L(Q,w,r) is

In the short run,a firm which has production function f(L,M) =4L^1/2M^1/2 must use 4 machines.If the cost of labor is $4 per unit and the cost of machines is $10 per unit,the short-run total cost of producing 72 units of output is