I haven't been able to answer this correctly, and neither has anyone I've shown, can you help me with this? **Production Function Analysis for a Home Remodeling Business**Suppose that the production function for Hannah and Sam's home remodeling business is defined by:\[ Q = f(L, K) \]\[ Q = 10L^{0.2}K^{0.3} \]Where:- $ Q $ is the output,- $ L $ is the labor input,- $ K $ is the capital input.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week.### a. Least-Cost Input Combination**Objective:** Determine the least-cost input combination for remodeling 100 square feet each week.**Instructions:** Round your answers to 2 decimal places.- **Labor Input:** 2.78 units- **Capital Input:** 16.73 units### b. Total Cost Calculation**Objective:** Calculate the total cost for the least-cost combination.**Instructions:** Round your answer to 2 decimal places.- **Total Cost:** $55,940**Note:** Ensure the use of precise rounding as calculations are sensitive to decimal adjustments.

The production function is the maximum set of output(s) that can be manufactured with a provided set of inputs. Utilization of a production function implies technical efficiency.A) Q = 10L0.2K0.3 Total cost, TC = wL + rK = 8000L + 2,000K For the least cost combination, MPL / MPK = w / r Or, MRTS(L, K) = w / r Given, MRTS = 2K / 3L Thus, 2K / 3L = 8000 / 2000 2K / 3L = 4 K = 12L / 2 = 6L If Q = 100, we have 10L0.2K0.3 = 100 L0.2K0.3 = 10 L0.2 * (6L)0.3 = 10 L0.5 * 1.712 = 10 L0.5 = 10 / 1.712 = 5.8419 Squaring both sides: L = 34.128 K = 6L = 6* 34.128 = 204.768 B) TC ($) = (8000 * 34.128) + (2,000 * 204.768) = 273,024 + 409,536 3) = $682,560

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Economics

Suppose that the production function for Hannah and Sam's home remodeling business is Q=FL.K) Q=10L0.2 0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and 16.73 units of capital. 2.78 b. What is the total cost? Instructions: Round your answer to 2 decimal places. $ 55940

Suppose that the production function for Hannah and Sam's home remodeling business is Q=FL.K) Q=10L0.2 0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and 16.73 units of capital. 2.78 b. What is the total cost? Instructions: Round your answer to 2 decimal places. $ 55940

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.

Question

I haven't been able to answer this correctly, and neither has anyone I've shown, can you help me with this?

**Production Function Analysis for a Home Remodeling Business**

Suppose that the production function for Hannah and Sam's home remodeling business is defined by:

\[ Q = f(L, K) \]
\[ Q = 10L^{0.2}K^{0.3} \]

Where:
- $ Q $ is the output,
- $ L $ is the labor input,
- $ K $ is the capital input.

Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week.

### a. Least-Cost Input Combination

**Objective:** Determine the least-cost input combination for remodeling 100 square feet each week.

**Instructions:** Round your answers to 2 decimal places.

- **Labor Input:** 2.78 units
- **Capital Input:** 16.73 units

### b. Total Cost Calculation

**Objective:** Calculate the total cost for the least-cost combination.

**Instructions:** Round your answer to 2 decimal places.

- **Total Cost:** $55,940

**Note:** Ensure the use of precise rounding as calculations are sensitive to decimal adjustments.

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