An electricity generating firm estimates its production function to be: Q = 10K(0.5) F(0.5) Where: Q = monthly electricity production measured in kilowatt hours K = machine hours (capital) per month F = fuel in gallons per month The rental cost of capital is $8 per machine hour and the cost of fuel is $4 per gallon.

State and illustrate the conditions that determine the firmâs cost minimizing use of fuel and capital.

Determine the firmâs optimal ratio of fuel to capital.

Suppose that this electricity firm is required by law to both operate within a fixed budget of $1200 per month as well as to produce enough that, at current prices, all demand is satisfied. It is estimated that current demand is 5,000 kilowatt hours.

Will the firm be able to satisfy both its budgetary and its demand requirements if it uses its inputs optimally?

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Hubert KochLv2

24 Aug 2019

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A price taking firm chooses its inputs to maximize short-run profits. Its Cobb-Douglass production function has the following form: q(L, K) = L^(1/2) K ^(1/3) . The output price is 1,000 per unit and the cost of each unit of input is 10. In the short-run, capital is fixed at 27 units.

(a) Set up the profit function in terms of labor only.

(b) Find the optimal choice of labor, L â .

Another price taking firm chooses its inputs to maximize long-run profits. Labor and capital are substitutes in production and both exhibit decreasing returns to scale, q(L, K) = L^(1/2) + K^(1/2) . The output price is 100 and the price of each of the inputs is 10.

(a) Set up the firmâs profit function and provide the two conditions for profit maximization.

(b) Find the profit maximizing levels of capital and labor.

rosearmadillo753

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)=L^0.3 K^0.7

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:

Q_d=60-10P+0.5I, Q_s=-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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