ECO440H5 Chapter Notes -Microeconomics, Sexually Transmitted Infection, Pareto Efficiency

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15 May 2014

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8. 1 adding up costs and benefits: the need for a conceptual basis. Efficiency in exchange: in a world of two individuals and two goods, individuals will trade the goods in order to maximizr the utility. They will do this until the marginal rate at which they are willing to substitute the goods (marginal rate of substitution, mrs) is equal to the ratio oif the prices of the goods. Thus, for efficient exchange, for any two individuals and any two goods. Efficiency in production: in a world of two factors of production, say equipment (k) and labor (l), production is efficient when the cost of the inputs is the lowest possible. Keeping output constant we can vary the proportions of equipment and labor. In most societies most goods and services are allocated through market processes. Using market mechanisms may remain the best available option even when the conditions for perfect markets are violated.

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3. A firm has a long-run production function:

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run?

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?

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1.Production efficiency.

A)state the condition for production in terms of which slopes are equal. use terms such as MRS,MRTS,MRT,and/or - P horizontal/P vertical P horizontal refers to the price of the good on the horizontal axis. Use subscripts and/or superscripts on MRS and MRTS as appropriate. In this case, P horizontal is the cost of labor (w)and P vertical is the cost of capital(r)

B) Draw an Edgeworth box for production efficiency. The K and L isoquants should show both inefficient ( crossing and efficient ( tangent) relationships.

C) Explain why points at isoquant intersection are inefficient. This answer has nothing to do with the answer to 1a above. The answer to this question is not whether the curves cross or are tangent but rather what happens to production levels at the same cost as production is moved to an efficient point on the contract curve.

D) State two governmental policies which could cause the production mix to remain at an inefficient point. This is the same as saying what policies could prevent the prices of the two factors of production(w/r) from adjusting to offer the same relative cost of inputs to all producers.

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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ECO440H5 Chapter Notes -Microeconomics, Sexually Transmitted Infection, Pareto Efficiency

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