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Deternining Output Level & Employment Equilibrium Point

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Problems are attached as PDF file as well.

Problems

1.The data in the following table give information about the price (in dollars) for which a firm can sell a unit of output and the total cost of production.

a)Fill in the blanks in the table.

b)Show what happens to the firm's output choice and profit if the price of the product falls from $60 to $50.

Q P R(at P=60) C(at P=60) Profit (at P=60) MC MR(at P=60) R(at P=50) Profit (at P=50)
0 60 100
1 60 150
2 60 178
3 60 198
4 60 212
5 60 230
6 60 250
7 60 272
8 60 310
9 60 355
10 60 410
11 60 475

2.Using the data in the above table, show what happens to the firm's ouput choice and profit if the fixed cost of production increases from $100 to $150 and then to $200. Assume that price of the output remains at $60 per unit. What general conclusion can you reach about the effects of fixed costs on the firm's output choice?

3.Use the same information as in Exercise 1.
a.Derive the firm's short-run supply curve.
b.If 100 identical firms are in the market, what is the industry supply curve?

4.In 1996, Congress raised the minimum wage from $4.25 per hour to $5.15 per hour, and then raised again in 2007. Some people suggested that a government subsidy could help employers finance the higher wage. This exercise examines the economics of a minimum wage and wage subsidies. Suppose the supply of low-skilled labor is given by
Ls=10w
Where Ls is quantity of low skilled labor (in millions of persons employed each year), and w is the wage rate (in dollars per hour). The demand for labor is given by
Ld= 80-10w
a.What will be the free-market wage rate and employment level? Should the government sets a minimum wage of $5 per hour. How many people would then be employed?
b.Suppose that instead of a minimum wage, the government pays a subsidy of $1 per hour for each employee, what will the total employment be now? What will the total level of employment be now? What will the equilibrium wage rate be?

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Solution Summary

There are four problems. Solution to first three problems determines the optimal output and profit level. It derives the firm's short-run supply curve. It also studies the effect of increase in fixed cost on optimal choice of production. Solution to last problem detemines the equilibrium employment level and wage rate. It also studies the effect of a subsidy on wage rate on equilibrium level.

Solution Preview

Please refer attached file for better clarity of tables and missing graphs.

Solution:

a) Fill in the blanks in the table

Price =$60 Price =$60
Q Cost=TC TR Profit=TR-TC MR* MC** TR=50*Q MR* Profit=TR-TC
0 100 0 -100 0 -100
1 150 60 -90 60 50 50 50 -100
2 178 120 -58 60 28 100 50 -78
3 198 180 -18 60 20 150 50 -48
4 212 240 28 60 14 200 50 -12
5 230 300 70 60 18 250 50 20
6 250 360 110 60 20 300 50 50
7 272 420 148 60 22 350 50 78
8 310 480 170 60 38 400 50 90
9 355 540 185 60 45 450 50 95 Optimal choice fot P=$50
10 410 600 190 60 55 500 50 90 Optimal choice fot P=$60
11 475 660 185 60 65 550 50 75
* MR=change in TR/change in output
** MC=change in TC/change in output

b)
We know that a firm sets its output such that MR>MC or MR=MC to maximize its profit.
Case 1
When Price=$60
We see that corresponding to Q=10, MR($60)>MC($55)
and corresponding to Q=11, MR($60)<MC($65)
So, firm will choose output level of 10 units with a profit of $190

Case 2
When Price=$50
We see that corresponding to Q=9, MR($50)>MC($45)
and ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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