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Ben and Geri have changed their production methods and are now producing ice cream according to the production function,

Y=KL,

1. The price of a machine is R= 2 dollars and a laborer costs W= 1 dollar, the expenditure level E=$8, Determine the slope of the iso-expenditure curve

2. By setting the MRTS equal to the slope of the iso-expenditure curve, determine the mascot-minimizing capital-labor ratio (K/L) with R=2 and W=1. Given that the firm wants to produce Y=8 units of output, what is the optimal level of capita and labor for the firm? what is the cost-minimizing level of expenditure E when the firm produces Y=8 pints of ice cream?

3.Suppose the price of a laborer goes up to W=2. What are the new cost-minimizing levels of capital and labor given that Ben and Geri are still producing Y=8 pints of ice cream? What is the new cost-minimizing level of expenditure

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Chika Ilonah
Chika IlonahLv10
28 Sep 2019

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Related questions

A manufacturing firm's production function is Q = KL + K + L. The price r of capital services is equal to 1, and let w denote the price of labor services. If the firm is required to produce 5 units of output, for what values of w would a cost-minimizing firm use

a) only labor?

b) only capital?

c) both labor and capital?

Suppose the process of producing lightweight parkas by Polly's Parkas is described by the function:

q = 40K0.6 (L-40)0.4

where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor. In addition to capital and labor, $10 worth of raw materials are used in the production of each parka.

Note that Eq/EK = 40(0.6) K -0.40 (L-40)0.4 and Eq/EL = 40K 0.6 (0.4) (L-40) -0.60

By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output (q), wage rates (w), and rental rates of machines (r).

The cost-minimizing demands for K and L are:

Use these results to derive the total cost function: that is, costs as a function of q, r, w, and the constant $10 per unit materials cost. The total cost function (TC) is:

2. This process requires skilled workers, who earn $64 per hour. The rental rate on the machines used in the process is $16 per hour. At these factor prices, what are total costs as a function of q.

Total costs (TC) are:

Does the technology exhibit decreasing, constant, or increasing returns to scale?

3. Polly's Parkas plans to produce 2000 parkas per week. At the factor prices given above, how many workers should the firm hire (at 40 hours per week) and how many machines should it rent?

The firm should use ___ worker hours.

The firm should use ___ machine hours.

What are the marginal and average costs at this level of production?

Marginal cost is $___ per unit of output.

Average cost is $___ .

A cost-minimizing firm has the following short-run production function:
Q=f (L,K)=72L+5L2-0.2L3

a) Briefly explain why this is a short-run production function.

b) At what level of employment would be diminishing returns set in for the variable input?

c) Fin the levels of employment that define stage two in the production process.

d)If the market-determined real wage rate is $20 determine the amount of labor a cost-minimizing firm would hire in order to minimize the total cost of production.

2) a) Briefly explain the concept of "Return to scale". What form of "Return toScale" does the following production function exhibit? Explain

b) Q=f(L,K)=L0.3 K0.7

Suppose a cost-minimizing firm wishes to change its scale of production and needs to know the combination of labor and capital to employ. If the first's total cost outlay is $14. Fin this combination using the information below and given that the prices of labor and capita are $1 and $3 per unit respectively.

Q= 0 1 2 3 4 5 6 7 8

TPI=0 11 20 28 35 41 45 46 46.5

TPK=0 24 45 63 78 87 93 96 97

where TPI AND TPK represent the total product of labor and total product of capital respectively.

3) Given the demand and supply schedules for semiconductors in a perfectly competitive market:

Qd=60-10P+0.5I, Qs=-10+4P-2C

Where I=average income of the demanders of this production

C=unit cost of the inputs used in the production of this commodity.

a) Find the expression for equilibrium price and equilibrium quantity transcended in this market.

b)Find the initial equilibrium and equilibrium quantity ifI=1000 and C=20

c) Determine the impact of an increase in income from 1000 to1200 on the initial equilibrium values.

d) Assume that an improvement in the technology of producing this commodity results in an increase in supply by a factor of 5, how will this development affect the initial equilibrium values?0

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