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ECON 2010 Lecture Notes - Lecture 15: Production Function, Marginal Product, Isocost

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School
Memorial University
Department
Economics
Course
ECON 2010
Professor
nikitalyssenko

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Document Summary

In the case of long-run production theory, all of the factors are free to change in order to produce output. This is really a planning period, rather than a production period. Firms are free to plan to alter any part of their production mix so as to be in a position to produce output at the lowest possible cost. However, the plans have to be separated from the requirement of actual production. When a producer is called upon to change the level of actual output, he must respond with whatever plant and equipment is currently available to him, which is then supplemented by changes in labour employment. This may lead the producer to plan to change the amount of plant and equipment. However, until the new adjusted quantity of plant and equipment is installed, it cannot be used in production.

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Related Questions

3. Firm Y uses labor and capital in production and the current time-period is too short for it to change the amount of equipment and work-space. However, it can change the level of its output by changing the amount of labor it uses, as shown here:

Labour 0 1 2 3 4 5 6

Output 0 12 22 30 36 40 42

A. Derive the marginal revenue product schedule given that the firm can sell each unit it produces for $10. (I.e., calculate the MRPL at each level of employment.)

B. Given that the price of each unit of output is $40 and each worker hired must be paid $40, what is the optimal level of employment of labour?

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 � 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?

The market for good X is perfectly competitive. The demand and supply functions of good X are given as follows: Demand: Qd = 6000 - 30 P Supply: Qs =500 + 20 P Qd is the quantity demanded in thousand units, Qs is the quantity supplied in thousand units, and P is the unit price in dollars for good X. Currently, there are 1000 identical profit-maximizing firms in the market and the production cost of each firm does not depend on the total number of firms in the market. Currently, the market is in long-run equilibrium.

a. What are the equilibrium market price and market quantity for good X? Briefly explain your answer.

b. What is the output of each firm in this long-run equilibrium? Briefly explain your answer.

c. Now suppose that the government requires each firm in this market to pay $10,000 company registration fee. After paying this fee, a firm can produce whatever output it wants. In other words, this fee will not change with the production of a firm.

i. Briefly explain how this registration fee will affect the market equilibrium output and price in the short run. ii. Briefly explain how this registration fee will affect the market equilibrium output and price in the long run.