Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 80L0.8K0.2 where I is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $100 and each unit of capital costs $400. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your
Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 80L0.8K0.2 where I is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $100 and each unit of capital costs $400. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your
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How many units of labor and capital should be purchased to maximize production? What is the maximum number of units of production?
![**Cobb-Douglas Production Function**
Suppose a Cobb-Douglas Production function is given by the following equation:
\[ P(L, K) = 80L^{0.8}K^{0.2} \]
where \( L \) is units of labor, \( K \) is units of capital, and \( P(L, K) \) is the total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $100 and each unit of capital costs $400. Further, suppose a total of $120,000 is available to be invested in labor and capital (combined).
### A) Maximizing Production Under Budget Constraints
**Question**: How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint?
- **Units of labor, \( L \)**: 600
- **Units of capital, \( K \)**: 150
### B) Maximum Production Units
**Question**: What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.)
- **Max production**: 36,377 units](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc05bac74-9392-4bb0-9ff6-f7e027936b2b%2Feba053f4-e57b-4fc5-ac3f-4f92762e23d2%2Fh99dwcn_processed.png&w=3840&q=75)
Transcribed Image Text:**Cobb-Douglas Production Function**
Suppose a Cobb-Douglas Production function is given by the following equation:
\[ P(L, K) = 80L^{0.8}K^{0.2} \]
where \( L \) is units of labor, \( K \) is units of capital, and \( P(L, K) \) is the total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $100 and each unit of capital costs $400. Further, suppose a total of $120,000 is available to be invested in labor and capital (combined).
### A) Maximizing Production Under Budget Constraints
**Question**: How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint?
- **Units of labor, \( L \)**: 600
- **Units of capital, \( K \)**: 150
### B) Maximum Production Units
**Question**: What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.)
- **Max production**: 36,377 units
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