1. Consider the following table that provides information for a firm’s short-run production function and its...

1. Consider the following table that provides information for a firm’s short-run production function and its product demand, given by the column labeled D1.

Labor	Output	Price (D₁)
0	0	$10.00
1	16	10.00
2	31	10.00
3	45	10.00
4	58	10.00
5	69	10.00
6	78	10.00

Based on that information, calculate Total Revenue (TR), Marginal Revenue Product (MRP), Marginal Product of Labor (MP) and Value of the Marginal Product (VMP), then answer the following questions:

Assume that the labor market is perfectly competitive. If the wage rate is $100, how many workers should the firm hire in order to achieve maximum profit?
Assume that the labor market is perfectly competitive. If the wage rate rises from $100 to $135, how many workers will the firm fire?
Based on your previous answers, what is the wage elasticity of this firm’s labor demand when wage increases from $100 to $135?
Assume that the labor market is perfectly competitive. Suppose the firm’s product demand is now given by the column labeled D₂. Calculate Total Revenue (TR), Marginal Revenue Product (MRP), Marginal Product of Labor (MP) and Value of the Marginal Product (VMP). If the wage rate is $100, how many workers should the firm hire in order to achieve maximum profit?

Labor	Output	Price (D₂)
0	0	$10.00
1	16	9.50
2	31	9.00
3	45	8.50
4	58	7.50
5	69	6.50
6	78	5.50

Expert Solution

TR = price * quantity. For example, when output = 16, TR = 16 * 10 = 160.
MR = Change in TR/ change in output. Fr example, when TR = 160, MR = (160-0)/ (1-0) = 160
MP = change in output. For the second worker, MP = 31 - 16 = 15.
VMP = MP*price. For example, for the second worker, VMP = 15 * 10 = 150

a. If the wage = $100, 5 workers will be hired.
When 5 workers are hired, VMP is greater than wage (110 > 100). For the next worker, VMP (90) is lower than the wage.

b. If wage = $135, 3 workers will be hired.
When 3 workers are hired, VMP (140) is greater than wage (135). For the next worker, VMP (130) is lower than the wage.

c. Elasticity of firm's labor = -1.14
E_L = %change in number of workers / % change in wage = 40% / -35% = -1.14

d. The new table:

If wage = $100, 3 workers will be hired.
When 3 workers are hired, VMP (119) is greater than wage. For the next worker, VMP (97.5) is lower than the wage.

Rahul Sunny answered 2 years ago

Explain the relationship between a firm’s short-run production function and its short-run cost function. Focus on...

Explain the relationship between a firm’s short-run production function and its short-run cost function. Focus on the marginal product of an input and the marginal cost of production. (p. 283 #3

Q- A firm’s short-run cost function for the production of gizmos is given by the following...

Q- A firm’s short-run cost function for the production of gizmos is given by the following expression: C(y) = 10y2 + 200y + 100 000. Draw the cost function C(y) and calculate; A- Calculate the range of output over which it would be profitable for this firm to produce gizmos if it can sell each gizmo for $2400. Calculate the value of the output that maximizes this profit. Calculate the value of maximum profit B- Repeat these calculations and explain...

Explain the relationship between a firm’s short-run production function and its shortrun cost function. Focus on...

Explain the relationship between a firm’s short-run production function and its shortrun cost function. Focus on the marginal product of an input and the marginal cost of production. b) A U.S. electronics firm is considering moving its production to a plant in Mexico. Its estimated production function is q=L 0.5 K 0. 5 . The U.S. factor prices are In Mexico, the wage is half that in the United States, but the firm faces the same cost of capital: ?...

Exercise 1. Firm Supply in the Short Run Consider a firm with the following production function:...

Exercise 1. Firm Supply in the Short Run Consider a firm with the following production function: y=L½K½. The cost function is C=w∙L+r∙K. In the short-run the input K is given at K=100. What is the short-run production function y(L)? Let w=0.1 and r=1. What is the cost function C(y)? Using the expression y(L) you found in part a, transform it into L(y) and plug it into the cost function C(L) to get C(y). Was a minimization necessary? Why or why...

9. a. Suppose that a firm’s production function is q=9x^1/2 in the short run, where there...

9. a. Suppose that a firm’s production function is q=9x^1/2 in the short run, where there are fixed costs of $1000, and x is the variable input whose cost is $4000 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). b. Write down the equation for the supply curve. c. If price is $1000, how many units will the firm produce? What is the level of...

7. Suppose your firm’s short-run production function is given as &nbs

7. Suppose your firm’s short-run production function is given as Labor Total Output 0 0 1 5 2 12 3 20 4 28 5 34 6 39 7 43 8 46 Assume that labor can be hired for $50 per worker and that your fixed cost is $1,000. a. What is the total variable cost of producing 5 units of output? b. What is the average variable cost of producing 12 units of output? c. What is the total cost of producing 20 units of output? d. What is the average total cost of producing...

Production/Cost Exercises 1. The following is a short-run production table for a firm with labor as...

Production/Cost Exercises 1. The following is a short-run production table for a firm with labor as its only variable input. Wage = $ 200 Capital = 100 units Capital Price= $40 Product Price= $120 Labor Output 0 0 1 50 2 110 3 160 4 200 5 230 6 250 7 260 8 265 9 260 10 250 a. Determine the following measures at all levels of output: MPL, APL, TFC, TVC, TC, TR, AVC, ATC, AFC, MC, PROFIT b....

Consider a toy making firm’s long run production choices. The following table shows the marginal products...

Consider a toy making firm’s long run production choices. The following table shows the marginal products of capital (K) and labour (L) for various methods of producing 10,000 toys per day. Production Method MPK MPL A 100 4 B 90 18 C 80 30 D 70 40 E 60 48 F 50 55 G 40 60 Capital costs $5.25 per unit and labour costs $3.00 per unit. a) Suppose the firm is currently producing 10,000 toys per day by using...

Short Run Cost Curves: Consider a firm with the following production function: q=(KL)/20 a. For a...

Short Run Cost Curves: Consider a firm with the following production function: q=(KL)/20 a. For a short-run situation in which K=10, wage = 4 and cost of capital = 1, derive expressions for short run total cost and short run average cost for this production function. b. Plot the short-run total cost curve and label it “TC1”. Now suppose that the cost of capital goes up to 2. (Continue to assume we’re in the short run and K can not...

The following table summarizes the short-run production function for your firm. Your product sells for $5...

The following table summarizes the short-run production function for your firm. Your product sells for $5 per unit, labor costs $5 per unit, and the rental price of capital is $20 per unit. Complete the following table, and then answer the accompanying questions. (1) (2) (3) (4) 5 6 L K Q MPL P VMPK 0 5 0 0 0 0 1 5 10 2 5 30 3 5 60 4 5 80 5 5 90 6 5 95 7...

Question