Economics 2150A/B Lecture Notes - Isocost, Fixed Cost, Mineral Water

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19 Apr 2014

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ECON 2150A/B Full Course Notes

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Lrtc shows how tc varies with output q holding input prices fixed and choosing inputs to minimize costs. Plot the lrtc curve from the lr cost minimization problem: lr total cost demoted by tc(q) shows how minimized total cost varies with holding input prices fixed and and selecting inputs to minimize output, cost. L* and k* are the input demand functions, which solve the lr cost minimization problem. Tc = w ( rq w )1 /2 ( wq r )1/2. Tc = 2w r q 1/2. The expression above is the lrtc curve and it tells you how tc vary with w,r, and q, the. One input price changes: q: how does lr cost vary when 1 input price changes? exogenous variables. An increase in the price of an input rotates the tc curve upward. It pivots down to c2 when the price of k rises.

Related Questions

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?

Q1) Soundscape Enterprises manufactures Sonoblast, a device that produces a high-pitched reminder to telemarketers that they have once again disturbed you just when you were sitting 1â2 down to dinner. The production function for Sonoblasts is given by the formula Q = 2KL where Q is in units of output per period, K is in machine-weeks per period, and L is in labour- weeks per period. The machine rental rate r is $512 per machine-week and the wage rate w is $128 per labour-week. In the short run, K is fixed at 4 machine-weeks per period.

a. Give the formulas for the short-run production function and the marginal product of labour (MPL) function.

b. Express variable cost (VC), total cost (TC), and marginal cost (MC) as functions of L and as functions of Q; and average variable cost (AVC), average fixed cost (AFC) and average total cost (ATC) as functions of Q.

c. At what level of Q is ATC minimized? What are the values of ATC and of MC at this level of output?

d. If K is increased to a fixed 16 units, at what level of Q is ATC minimized, and what are the values of ATC and of MC at this level of output?

e. In the long run, with all inputs variable, what is the optimal K/L ration with input prices unchanged? How many units of L and of K would be required to produce the levels of output in 1c and in 1d and what is the average cost of producing Sonoblasts in each case? Explain the relation between your results here and those for 1c and 1d.

lilacchinchilla474

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. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. a) What is the total cost function for your plant—namely, how much would it cost to produce q engines? What are average and marginal costs for producing q engines? How do average costs vary with output? (Clue: the total cost function should be defined in terms ONLY of output, q) b) How many teams are required to produce 250 engines? What is the average cost per engine? c) 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? (Clue: to calculate the MRTS of labor for capital --as the ratio of marginal products of the two inputs—and, afterwards, to equal the MRTS to the ratio of input prices).

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Economics 2150A/B Lecture Notes - Isocost, Fixed Cost, Mineral Water

ECON 2150A/B Full Course Notes

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