Asked by ashlee clowers on May 06, 2024
Verified
the production function is f(x1, x2) x1/21x1/22.If the price of factor 1 is $8 and the price of factor 2 is $4, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?
A) We can't tell without knowing the price of output.
B) x1 x2.
C) x1 0.50x2.
D) x1 2x2.
E) x1 4x2.
Proportions
The relationship between parts and a whole, often expressed as a ratio or fraction.
Factor 1
An element or component that contributes to a particular result or situation; can be considered as a contributing variable in different contexts.
Profit
The financial gain obtained when the revenue from selling goods or services exceeds the costs involved in their production or provision.
- Apply production function methodologies to calculate the perfect amounts of inputs to maximize profits.
- Discern the relationship among input costs, the valuation of outputs, and the elevation of profit levels to their maximum.
- Establish the ideal mix of several inputs by evaluating their associated costs and the function of production.
Verified Answer
GM
Gavin MahanMay 09, 2024
Final Answer :
C
Explanation :
To maximize profits, the firm should use the ratio of factor 1 to factor 2 that gives the highest marginal product of each factor per dollar of expenditure. In other words, the firm should allocate its resources such that the marginal product per dollar is the same for both factors.
The marginal product of factor 1 is:
MP1 = (1/2)x1/22
The marginal product of factor 2 is:
MP2 = x1/21
The ratios should be such that:
MP1/$8 = MP2/$4
Simplifying:
MP1/2 = MP2
Substituting the marginal products:
(1/2)x1/22 = x1/21
Simplifying further:
x1 / 2x2 = 1/2
x1 = 0.5x2
Therefore, the optimal ratio of factor 1 to factor 2 is 1:0.5 or 2:1.
The marginal product of factor 1 is:
MP1 = (1/2)x1/22
The marginal product of factor 2 is:
MP2 = x1/21
The ratios should be such that:
MP1/$8 = MP2/$4
Simplifying:
MP1/2 = MP2
Substituting the marginal products:
(1/2)x1/22 = x1/21
Simplifying further:
x1 / 2x2 = 1/2
x1 = 0.5x2
Therefore, the optimal ratio of factor 1 to factor 2 is 1:0.5 or 2:1.
Learning Objectives
- Apply production function methodologies to calculate the perfect amounts of inputs to maximize profits.
- Discern the relationship among input costs, the valuation of outputs, and the elevation of profit levels to their maximum.
- Establish the ideal mix of several inputs by evaluating their associated costs and the function of production.