Asked by Gustavo Perez-Ramirez on Jun 15, 2024
Verified
the production function is given by F(L) 6L2/3.Suppose that the cost per unit of labor is $8 and the price of output is 4, how many units of labor will the firm hire?
A) 16
B) 8
C) 4
D) 24
E) None of the above.
Production Function
A mathematical representation that describes the relationship between inputs used in production and the resulting output.
Output
The aggregate sum of products or services generated by a business, sector, or economic system.
Cost
The value of everything a company gives up to produce goods or services, including materials, labor, and overhead expenses.
- Gather insights on the causal relationship between the costs associated with inputs, the pricing of products, and the maximization of profit.
- Put production functions into practice to calculate the optimum input amounts for maximizing financial gains.
- Quantify the impact of price changes in inputs and outputs on achieving optimal input levels for profit maximization.
Verified Answer
CG
Courtney GreenJun 22, 2024
Final Answer :
B
Explanation :
To maximize profit, the firm will hire labor up to the point where the marginal product of labor (MPL) equals the wage rate. The MPL can be found by taking the derivative of the production function with respect to labor, which gives:
MPL = 62/3
Plugging in the given values for the price of output and cost per unit of labor, we get:
MPL = 6S1U11/3S1S1
To find the level of labor that maximizes profit, we need to equate MPL with the wage rate. Since the wage rate is $8 per unit of labor, we have:
MPL = 8
6S1U11/3S1S1 = 8
Solving for L, we get:
L = ( 6S1U11/3S1S1)/(8)
Plugging in the given values, we get:
L = (4*6*1*1^(1/3))/(8)
L = 8
Therefore, the firm will hire 8 units of labor to maximize profit.
MPL = 62/3
Plugging in the given values for the price of output and cost per unit of labor, we get:
MPL = 6S1U11/3S1S1
To find the level of labor that maximizes profit, we need to equate MPL with the wage rate. Since the wage rate is $8 per unit of labor, we have:
MPL = 8
6S1U11/3S1S1 = 8
Solving for L, we get:
L = ( 6S1U11/3S1S1)/(8)
Plugging in the given values, we get:
L = (4*6*1*1^(1/3))/(8)
L = 8
Therefore, the firm will hire 8 units of labor to maximize profit.
Learning Objectives
- Gather insights on the causal relationship between the costs associated with inputs, the pricing of products, and the maximization of profit.
- Put production functions into practice to calculate the optimum input amounts for maximizing financial gains.
- Quantify the impact of price changes in inputs and outputs on achieving optimal input levels for profit maximization.