Given the Production Function of a perfectly competitive firm: Q = 80L + 10L2 - L3,...
- Given the Production Function of a perfectly competitive firm: Q = 80L + 10L2 - L3, where Q =
Output and L = labor input
a. At what value of L will Diminishing Returns take effect?
b. Calculate the range of values for labor over which stages I, II, and III occur?
c. Suppose that the wage rate is $30 and the price of output is $2 per unit. How many workers should
the firm hire?
d. At what value of L will Q be at its maximum? What is the maximum amount of Q?
e. If demand forecasts predict an output level of between 400 and 450 in the next decade, what would
be your long-run strategy to optimize the resources of your company?
Homework Answers
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Given the Production Function of a perfectly competitive firm:
Q = 80L + 10L2 - L3,...
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Q9. A perfectly competitive firm operates in the short-run with labor as its only variable factor. Its production function is: Q = -L3 + 10L2 + 88L where Q is output per week measured in tons and L is the number of workers employed. The weekly wage is $324 and the product sells for $3.24 per ton. (a) At what weekly output is marginal cost equal to average variable cost? (b) What is the minimum product price...
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29. A firm produces in a perfectly competitive market and hires labor in a perfectly competitive labor market. The firm hires four workers, the marginal product of the fourth worker is 4, and the wage rate is $40. The firm produces 100 units of the product, which sell for a price of $10. This firm is a. maximizing profit when it hires four workers. b. not maximizing profit and should hire more workers to increase profit. c. not maximizing profit...
(d) A perfectly competitive firm has the following production function: Q=L The price of labor is...
(d) A perfectly competitive firm has the following production function: Q=L The price of labor is equal to w. If the firm maximizes profit and the price, p, is equal to 4w, then the firm will supply 2 units of output and profit is equal to 4w.
Leadbelly Co. Sells pencils in a perfectly competitive product market and hires in a perfectly competitive...
Leadbelly Co. Sells pencils in a perfectly competitive product
market and hires in a perfectly competitive labor market. assume
that the market wage rate for workers is $150 per day.
A.
What rule should Leadbelly follow to hire the profit-maximizing
amount of labor?
B.
At the profit-maximizing level of output, the marginal product of
the last work or hired is 30 boxes of pencils per day. Calculate
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C.
Draw a diagram of the...
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Suppose that a firm is producing in the short run with output given by: Q = 75L-L2 The firm hires laborat a wage of $32 per hour and sells the good in a competitive market at P = $24 per unit. Now suppose that a firm is looking to maximize Total Revenue (not Total Profit) How many workers (L) should the firm hire? Enter as a value. ROUND TO THE NEAREST WHOLE NUMBER.
Competitive Firms - Optimal Labor and Capital 1. A competitive firm has production technology q A...
Competitive Firms - Optimal Labor and Capital
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A perfectly competitive firm uses a single input (labor) to produce a good according to a...
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(d) A perfectly competitive firm has the following production function: Q=L The price of labor is equal to w. If the firm maximizes profit and the price, p, is equal to 4w, then the firm will supply 2 units of output and profit is equal to 4w.
Leadbelly Co. Sells pencils in a perfectly competitive product
market and hires in a perfectly competitive labor market. assume
that the market wage rate for workers is $150 per day.
A.
What rule should Leadbelly follow to hire the profit-maximizing
amount of labor?
B.
At the profit-maximizing level of output, the marginal product of
the last work or hired is 30 boxes of pencils per day. Calculate
the Price of a box of pencils.
C.
Draw a diagram of the...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
Suppose that a firm is producing in the short run with output given by: Q = 75L-L2 The firm hires laborat a wage of $32 per hour and sells the good in a competitive market at P = $24 per unit. Now suppose that a firm is looking to maximize Total Revenue (not Total Profit) How many workers (L) should the firm hire? Enter as a value. ROUND TO THE NEAREST WHOLE NUMBER.
Competitive Firms - Optimal Labor and Capital
1. A competitive firm has production technology q A K La. lt can sell output at price P and hire capital and labor at competitive factor prices r and w. Write down the firm's profit maximization problem. What are the firm's first- order necessary conditions for a maximum. a. w Suppose now that α-,P-1 and -1. b. What is the firm's optimum capital labor-intensity? Why can't the optimum scale of production q be...
A perfectly competitive firm uses a single input (labor) to produce a good according to a production function Q(L) = 2/7 , where Lis the amount of labor it uses. The good sells for $180 per unit (price). The input costs $15 per unit (wage). 1. (20 pts) What is the profit-maximizing amount of input (L)? 2. (10 pts) What is the profit-maximizing amount of output (Q)? 3. (10 pts) How much profit does the firm make when it maximizes...
Suppose that a firm had a production function given by q-21 K The rental rate for the fim is $10 and the wage is s5 Solve the optimization condition for K and then fill in the value that appears in front of L K- Round to the nearest 2 decimal places if necessary.) Suppose that a firm had a production function given by q-L025k075. The wage rate (w) is $10 and the rental rate () is $10 Calculate the amount...
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