Exam 33:Production-Part A

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The marginal rate of transformation between two goods indicates the rate at which an efficient economy would have to give up one good to obtain more of the other.

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If there are constant returns to scale in an industry,then in competitive equilibrium,profits in that industry must necessarily be zero.

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A small company produces two goods,swords and plowshares.The company has 100 type alpha employees and 100 type beta employees.If an alpha devotes all his time to producing swords,he can make 2 swords per week.If he devotes all his time to producing plowshares,he can make 4 plowshares per week.A beta can produce either 1 plowshare per week or 1 sword per week.The company wants to produce 218 swords and as many plowshares as it can.How many type betas should it employ at making swords?

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On a certain island there are only two goods,wheat and milk.The only scarce resource is land.There are 1,000 acres of land.An acre of land will produce either 3 units of milk or 32 units of wheat.Some citizens have lots of land;some have just a little bit.The citizens of the island all have utility functions of the form U(M,W)= MW.At every Pareto optimal allocation,

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When there is production,a competitive equilibrium is not Pareto optimal unless there are increasing returns to scale.

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Tip can write 3 pages of term paper or solve 9 workbook problems in an hour,while Spot can write 4 pages of term paper or solve 4 workbook problems in an hour.If they each decide to work a total of 7 hours and to share their output,then if they produce as many pages of term paper as possible given that they produce 18 workbook problems,

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Al and Bill are the only workers in a small factory which makes geegaws and doodads.Al can make 4 geegaws per hour or 12 doodads per hour.Bill can make 2 geegaws per hour or 8 doodads per hour.Assuming that neither of them finds one task more odious than the other,

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Robinson Crusoe has exactly 8 hours per day to spend gathering coconuts or catching fish.He can catch 3 fish per hour or he can pick 6 coconuts per hour.His utility function is U(F,C)= FC,where F is his consumption of fish and C is his consumption of coconuts.If he allocates his time in the best possible way between catching fish and picking coconuts,his consumption will be the same as it would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1.

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On a certain island there are only two goods,wheat and milk.The only scarce resource is land.There are 1,000 acres of land.An acre of land will produce either 14 units of milk or 15 units of wheat.Some citizens have lots of land;some have just a little bit.The citizens of the island all have utility functions of the form U(M,W)= MW.At every Pareto optimal allocation,

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For each carload of ore removed from the Matchless Mine,1 pound of lead and 1 ounce of silver is smelted.The cost of mining and processing 1 carload of ore is C(Q)= 400 + 2Q + 0.04Q2.The demand for silver (per ounce)is Ps= 30 -0.30Qs and the demand for lead (per pound)is Pl =6 -0.02Ql.What should the owners of the Matchless Mine do to maximize profits (in the long run)?

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Robinson Crusoe spends 4 hours a day catching fish and picking coconuts.He can always catch 2 fish per hour and he can always gather 3 coconuts per hour.His utility function is CF,where C is the number of coconuts he eats per day and F is the number of fish he eats per day.How many fish will he choose to eat per day?

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Tip can write 2 pages of term paper or solve 2 workbook problems in an hour,while Spot can write 2 pages of term paper or solve 6 workbook problems in an hour.If they each decide to work a total of 8 hours and to share their output,then if they produce as many pages of term paper as possible given that they produce 14 workbook problems,

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In the process of producing 1 hormone-free,stress-free,happy cow,the New Age Cattle Ranch produces 1 ton of natural,organic plant fertilizer.Demand for the ranch's cattle is given by Pc= 2,000 -5Qc,and demand for fertilizer is given by Pf = 500 -2Qf.The cost of producing Q cow-fertilizer bundles is C =5,000+200Q.To maximize profits,the ranch should

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Mandy is a master wood-carver and Jerry is her apprentice.They will each work the same number of hours making toy cars.Each car requires 4 wheels and 1 body.Mandy makes wheels at the rate of 25 per hour and bodies at the rate of 10 per hour.Jerry makes wheels at the rate of 10 per hour and bodies at the rate of 10 per hour.If they wish to maximize output,how many wheels should Jerry make per hour?

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