ECO100Y5 Chapter Notes - Chapter 8: Profit Maximization, Marginal Product

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Chapter 8 notes producers in the long run. To maximize proits in long run should select producion method that produces output at lowest cost. Raio of marginal products on let side compares contribuion to output of last unit of capital and last unit of labour. If raio on let side was less, it would pay irm to switch to method of producion that uses less labour and more capital: when raio is equal, most cost-minimizing method. Pos; methods of producion will change if relaive prices of inputs change, with relaively more of cheaper input and relaively less of more expensive input being used. Firms moivated to use less of factors that are more scarce to economy and more factors that are abundant. Long run average cost; curve showing lowest possible cost of producing each level of output when all inputs can be varied. Determined by current technology and prices of factors of producion.

Related Questions

The long-run production function for a rm's product is given by q = f(K; L) = 5 K L. The price of capital is $10 and the price of labor is $15.
a. Suppose the rm wishes to produce output of 500. List 5 combinations of capital and labor that the rm can transform into 500 output.
b. For each of your 5 combinations from part a, give the cost of using that combination of capital and labor. Which is the lowest?
c. For your lowest cost combination from part b, calculate the marginal product of capital (MPK) and the marginal product of labor (MPL).
d. For your answer in parts b-c, is your marginal product per dollar equal across the two inputs.

taupeduck74

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

You manage a plant that mass-produces engines by teams of workers using assembly

machines. The technology is summarized by the production function

q = 5 KL

where q is the number of engines per week, K is the number of assembly machines, and L

is the number of labor teams. Each assembly machine rents for r = $10,000 per week, and

each team costs w = $5000 per week. Your plant has a fixed installation of 5assembly machines as part of its design.

In the SHORT RUN:

For any given level of output q, write the expression for the number of Labor teams required.

b. What is the cost function for your plant ï¿½ namely, how much would it cost to produce q engines? (Hint: TC=TFC+TVC, TFC=rK, TVC=wL)

c. What are average and marginal costs for producing q engines? How do average costs vary with output?

d. How many Labor teams are required to produce 250 engines? What is the average cost per engine?

In the LONG RUN:

e. You are asked to make recommendations for the design of a new production facility. What capital/labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q? MPL=5K, MPK=5L.

f. For output q=500, how many L and K should you use in order to minimize cost?

g. What is the minimum cost of production for q=500?

h. What is the minimum cost of product for any output q? (Note: write TC as a function of q).

i. If w is increased to $10,000 per week, how does this change the capital/labor (K/L) ratio if you want to minimize the total cost of production?

j. Given the new wage rate, how many L and K should you use in order to minimize cost for output q=500?

k. Is the expansion path a straight or a curved line? Is it upward or downward sloping? Why?

ECO100Y5 Chapter Notes - Chapter 8: Profit Maximization, Marginal Product

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