Economics 2150A/B Lecture Notes - Lecture 7: Isocost, Tangent, Isoquant

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ECON 2150A/B Full Course Notes

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In a firm there are 2 homogenous inputs; labour and capital. Each firm has a desired output and a desired total cost allocated. Isocost line is a set of combinations of labour and capital that will result in the same total cost of the firm. Iocost line like a budget line is a straight downward sloping line with a slope listed above and y intercept tc/r and x intercept tc/w. Interior solution allows you to derive the interior optimum which is the optimal input basket at a point where the isocost line is just tangent to the isoquant line. It is the rate at which a producer would be willing to echange k for l and keep the same desired cost in the market place. For a cob douglas bundle, mrts is ak/bl. A consumer can keep the same costs from bundle a if he traded in one unit of k for 1 or more units of l.

Related Questions

A firm has a production function Q=F(K, L) with the constant return to scale, where k is units of capital and L is united of labour. Input prices are r=$2 per unit of K and w=$1 per unit of L. When it produces 5 units of output, it uses 2 units of capital and 3 units of labour. When its long-run total cost is equal to $70, how much capital and labour it will employ to product how many units of output? What is the long-run average cost?

lavenderwolf32

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?

You are an efficiency expert hired by a firm in the clothing industry that uses machines (K) and workers (L) as inputs. The firm has estimated that the marginal product of labor is MPL = 120 - 4 L, while the marginal product of capital is MPK = 50 - 5 K. The firm is currently using 25 units of L and 7 units of K. If w = $20, r = $15 then

a. the firm is minimizing the cost of producing the given quantity of output.

b. the firm should use less L and more K to minimize the cost of producing the given quantity of output

c. the firm should use less K and more L to minimize the cost of producing the given quantity of output

d. the firm is profit maximizing but not cost minimizing

amberhornet175

Economics 2150A/B Lecture Notes - Lecture 7: Isocost, Tangent, Isoquant

ECON 2150A/B Full Course Notes

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