Exam 21:Cost Minimization-Part A

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'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 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?

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

As head of the planning commission of Eastern Motors,your job is to determine where to locate a new plant.The only inputs used in your cars are steel and labor and the production function is Cobb-Douglas where f (S,L)= S.5L.5,where S is tons of steel and L is units of labor.You can locate your plant either in country A or country B.In country A,steel costs $7 a ton and labor costs $7 per unit.In country B,steel costs $8 per ton and labor costs $6 per unit.In which country should the company locate its new plant so as to minimize costs per unit of output?

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 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

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

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?

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,T/5},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 $200 per hour,while paint costs $40 per tube.Using a $10,000 grant from the National Endowment for the Arts,how many hours of "living sculpture" can Mr.Smudge create?

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?

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?

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?

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

If the production function for tuna casseroles is min{x1,x2 2},where x1 is the amount of factor 1 and x2 is the amount of factor x2,find the cost function for tuna casseroles.

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 conditional factor demand function for factor 1 is a function x1(w1,w2,y)that tells the ratio of price to output for an optimal factor choice of the firm.

A competitive firm uses two inputs,x and y.Total output is the square root of x times the square root of y.The price of x is $17 and the price of y is $11.The company minimizes its costs per unit of output and spends $517 on x.How much does it spend on y?