Question 1

Standale Plastics produces plastic dustpans,using a semi-automated system of five machines to produce pans.The amount of labor to tend the machines,repair,adjust input flows,and remove completed pans,is variable,and output tends to follow the formula: Q = 300L^0.6,where Q = units of output produced per day and L = number of daily workers. (a)Compute the total product per day and the marginal product of labor for the first five workers.

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Question 2

A firm produces according to the following production function: Q = K0.25L0.75,where Q = units of output,K = units of capital,and L = units of labor.Suppose that the price of K is $4 per unit,and the price of L is $6 per unit.What is the optimal capital/labor ratio?

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Question 3

A firm has carefully estimated its production function to be: Q = K0.55L0.45,where Q = units of output,K = units of capital,and L = units of labor.What is output elasticity in this case? What sort of returns to scale does the firm face? Explain.

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Question 4

Specialty Steel has carefully measured production in its new plant to determine whether it is technically efficient in production.It has found that,for its two inputs K and L,it has the following marginal products: MPK = 15 units and MPL = 22 units.The inputs are hired in perfectly competitive markets,and the firm faces input costs of PK = $7.50 and PL = $10 per unit.
You have been hired as a consultant to assist Specialty in increasing profitability.What do you recommend about production planning? Explain.

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Question 5

Ranger Construction is preparing to repair potholes,under contract to the local county road repair agency.Based on past experience,Ranger has found that output can be described by: Q = K0.5L0.5,where Q = pot holes filled,K = units of capital,and L = units of labor.Ranger can hire labor at $12 per hour,and the cost of capital is $8 per unit.Capacity limitations require that Ranger accepts no more than $96,000 worth of filling this season.What is the optimal mix of inputs for Ranger? How many potholes should Ranger agree to fill? Use the method of Lagrange multipliers to find the solution.

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Question 6

Enpar manufactures engine parts for an automotive manufacturer.It operates two plants,A and B,which have the following production functions: QA = 30SA - 0.25SA2 and QB = 40SB - 0.5SB2,where QA and QB denote the outputs of engine parts from each plant and SA and SB denote the amounts of steel used in each plant.Suppose that total steel availability is 40 units.What is the optimal allocation of steel between the two plants?

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Question 7

Sleak Teak builds yard furniture,using domestic hardwoods and (in a smaller shop)handcrafted knick-knacks from the same sort of wood.Although hardwoods were readily available in the past,recently they have been much more difficult to obtain.Consultation with the plant managers of the two lines has resulted in the following production functions for hardwood usage in the two products: Yard furniture: Y = 2T_Y - 0.001T_Y² Knick-knack: K = 20T_K - 0.01T_K², where Y and K denote units of the two types of products and T_Y and T_K denote teak used in yard furniture and knick-knacks respectively.Yard furniture can be sold at a profit of $100 per unit,and knick-knacks can be sold at a profit of $25 each.Sleak Teak has 1,300 units of teak available.How should it be allocated across the two products? Explain.

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Question 8

Carefully explain the condition that the firm should follow if it wishes to produce at least cost in the long run.

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Question 9

Assume that a firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital.Given that the production function is given by: Q = 10L - L2 + 60K -1.5K2,where Q is total output,L is labor,and K is capital,what is the firm's optimal combination of capital and labor?

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Question 10

A firm produces a good in two factories: one in Tucson and one in Phoenix.Historically,the plants' long-run average costs have been comparable.Engineers have found that output elasticity at the Tucson plant is 1.1,while at Phoenix it is 0.93.A senior production manager has recommended expanding the scale of production in Tucson over the next few years and cutting production in Phoenix.Examine the validity of this proposal.

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Question 11

Crew Brew produces a popular brand of beer in its mini-brewery located on a small river in Wisconsin.It uses a special formula,combined with the fresh water from the local stream,to produce a drink popular with local folks and tourists who visit during the summer fishing season,and autumn deer hunting season.The production function of Crew follows the formula:
Q = 50K + 50L,where Q = barrels of beer,K = units of capital,and L = units of labor.
(a)Suppose that capital can be purchased for $8 per unit,and labor costs $6 per unit.What is the optimal combination of inputs for the firm to employ?

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Quiz 5: Production

A firm produces according to the following production function: Q = K0.25L0.75,where Q = units of output,K = units of capital,and L = units of labor.Suppose that the price of K is $4 per unit,and the price of L is $6 per unit.What is the optimal capital/labor ratio?

A firm has carefully estimated its production function to be: Q = K0.55L0.45,where Q = units of output,K = units of capital,and L = units of labor.What is output elasticity in this case? What sort of returns to scale does the firm face? Explain.

Carefully explain the condition that the firm should follow if it wishes to produce at least cost in the long run.