ENGR.ECONOMIC ANALYSIS
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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](https://content.bartleby.com/qna-images/question/c05bac74-9392-4bb0-9ff6-f7e027936b2b/eba053f4-e57b-4fc5-ac3f-4f92762e23d2/h99dwcn_processed.png)
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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- Which graph depicts a technological breakthrough in the production of Y only?arrow_forwardThe quantity, Q, of a certain product manufactured depends on the quantity of labor, L, and of capital, K, used according to the function 0 = 900LK¹³. Labor costs $100 per unit and capital costs $50 per unit. What combination of labor and capital should be used to produce 36,000 units of the goods at minimum cost? What is that minimum cost? Round your answers to two decimal places.arrow_forwardCom 120.000 D 80.000 40.000 Robots 5.000 10.000 15.000 In the graph above, the resources in this economy arearrow_forward
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