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# Analyzing the isoquant and isocost curves

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Consider the following graph, and answer questions a through e.

Please see the attached MS Word document for the graph.

a. If the price of capital is \$7.50 per unit what is the per unit price of labor?
b. How many units of labor should the firm use in order to produce 400 units of output at the least cost?
c. The minimum cost of producing 800 units of output is what?
d. How many units of capital should the firm use to produce 800 units of output at the lowest cost?
e. The minimum cost of producing 1,200 units of output is what?

https://brainmass.com/economics/output-and-costs/533970

#### Solution Preview

a. If the price of capital is \$7.50 per unit what is the per unit price of labor?
Please refer to the isocost line, which is tangent to isoquant curve pertaining to output of 400 units,
Total cost=Maximum units of capital*price of capital=200*7.50=\$1500
Per unit price of labor=Total Cost/Maximum units of labor=1500/300=\$5

b. How many units of labor should the firm use in order to produce 400 units of output at the least cost?
Point at which isocost line is ...

#### Solution Summary

Solution depicts the steps to determine labor and capital units at a given output level with the help of given diagram.

\$2.19

## Input Price Changes and Isocost-Isoquant Analysis; Long-Run Competitive Equilibrium

1 ( Production-Cost Duality)
If all firms in an industry have constant returns-to-scale production functions, what can we say about the efficient (e.g. cost-minimizing) plant size in the long-run?

2 (Input Price Changes and Isocost-Isoquant Analysis)

Given the recent economic slowdown, a number of policy makers have advocated the adoption of investment tax credits (ITCs), which effectively lower the price of capital to firms.

Southeastern Wisconsin has a large metal fabrication industry, which hires machinists as skilled labor and uses various machines (lathes, presses, grinders, etc.) as its capital stock. In the short-run, metal fabricators have a fixed stock of capital, but in the long-run, their capital stock can be varied.

An economist with the Southeastern Wisconsin Economic Development Agency is interested in estimating how much a proposed federal Investment Tax Credit that will generate a 25 percent reduction in the cost/price of capital (e.g. the rental rate of
capital, r , will fall by 25 percent, will affect output and employment in Wisconsin's metal fabrication industry.

From previous estimates of firm-level production functions for the metal fabricating industry, the economist knows that the typical firm's production function exhibits constant returns to scale, but has a low elasticity of substitution of labor for capital. A graphical characterization of the production isoquant is as follows {see attachment}

Question 2, continued: A union official stridently opposes the Investment Tax Credit, stating that the immediate effect of the policy will be to destroy jobs in the metal fabrication industry.

The economist working for the Southeastern Wisconsin Economic Development Agency has asked for your input regarding the claims of the union official. Describe the likely long-run effects of the Investment Tax Credit on output and labor and capital utilization, both in words and using isoquant-isocost analysis. Make sure that the analysis of the long-run effect of the Investment Tax Credit is thorough.

5 (Long-Run Competitive Equilibrium)
We wish to understand why, in the last ten years, the price of personal computers has gone down and the quantity produced has increased.

Consider the following facts listed below. For purposes of this problem, simply take these facts as given and do not bring in/draw upon information not presented in this list of facts. [Throughout the problem, you may assume that the firm purchases inputs to production in perfectly competitive input markets, so each firm faces input supply schedules that are perfectly elastic (horizontal).]

Fact 1: The personal computer market is a perfectly competitive market. [This means that price = marginal cost = minimum average total cost in long-run equilibrium, and that there is free entry and exit. In the product market, the firm takes the price of personal computers as given (faces a horizontal demand curve.)]

Fact 2: Entry of new firms into the personal computer industry does not affect the price of inputs used by the industry. [This means that the personal computer industry is characterized as a constant-cost industry.]

Fact 3: Personal computers have become more popular in the last ten years. [In the market for personal computers, the industry demand curve has shifted out (demand has increased).]

Fact 4: The cost of production for computers has decreased due to technological innovations.

Suppose the personal computer market was in an initial long-run equilibrium ten years ago and is in a long-run equilibrium today. Use long-run equilibrium analysis to answer the following questions.

Question 5.1: Can you explain the data (increase in production and decrease in prices) using the first three facts (Facts 1,2 and 3) mentioned above?

Question 5.2: Can you explain the data based only on Facts 1,2 and 4 mentioned above?

Question 5.3: Answer the question posed in Question 5.2 above again, but instead of supposing the personal computer industry is a constant-cost industry, this time suppose the personal computer industry is a decreasing-cost industry.

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