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ECON-200 Lecture Notes - Lecture 25: Record Producer, Isoquant, Price Ceiling

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School
Diablo Valley College
Department
Economics
Course
ECON-200
Professor
Sorce

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Document Summary

Econ-200 factors of production - inputs that firm uses to produce. Mainly divided into labor, materials, capital: capital - not just money, but also equipment, buildings, machinery production function - shows highest output for combo of inputs. Ultimately helps the producers: sort of like a combination of a price ceiling (limits supply for sure) and price floor (leads to an additional producer surplus for the most part) Producer surplus increases by a, decreases by c. Net change = loss of b+c (deadweight) import restrictions - either w/ tariff (tax) or quota, serves to help domestic market. W/o quotas, domestic consumers would buy solely/mostly from abroad instead of domestic markets to keep domestic markets alive, consumer surplus must suffer. Domestic markets want the quota to be 0, or for tariffs to be so high that foreign producers won"t interfere w/ domestic market: decreases competition, increases price >> increases revenue, all at the expense of the consumer.

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Related Questions

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?

For each of the following assertions, please indicate whether they are true or false. No credit will be given without an explanation as to why your claim is correct.

(a) (4 points) There are two firms: one has production function f (K, L) = K + L and the other has production function f?(K,L) = (K+L)2 ?50. Assertion: These two firms have the same shaped isoquants, but different technology.

(b) (4 points) Assertion: In the short run, if the marginal product of labor curve is decreasing, then it is below the average product of labor curve.

(c) (4 points) A T-shirt company can make 1000 T-shirts with 2 workers and 1 machine. It continues to make 1000 T-shirts if it has more than 2 workers but only 1 machine or 2 workers and more than 1 machine. The company currently produces 1000 shirts per month for its single customer. The price of capital falls, but the firm must still produce 1000 shirts per month. Let all inputs be variable. Assertion: The firm will not hire or fire any workers.

(d) (4 points) A technology firm has a Cobb Douglas production function and measures the marginal rate of technical substitution (MRTSLK) at MPL/MPK = 3. The prices of labor and capital faced by the firm are such that currently W/R = 2. Assertion: The tech firm can lower costs (holding output fixed) by laying off some of its labor force and using more capital.

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).