### Cost Minimization in Production#### Problem Description**Scenario:**A firm's production function is defined by $ Q = 2KL $, where:- $ Q $ is the quantity of output,- $ K $ is the units of capital,- $ L $ is the units of labor.**Additional Information:**- The marginal product of labor (MPL) is equal to capital $ K $,- The marginal product of capital (MPK) is equal to labor $ L $.**Cost Information:**- The price per unit of labor (wage) is $30,- The price per unit of capital is $50.#### ObjectiveThe goal is to determine the combination of labor and capital that minimizes the cost of producing 480 units of output.#### Given Options- $ L = 10 $, $ K = 24 $- $ L = 12 $, $ K = 20 $- $ L = 20 $, $ K = 12 $- $ L = 24 $, $ K = 10 $#### QuestionWhich combination of labor and capital should the firm use to produce 480 units of output at the minimum cost?#### Analysis1. **Production Function Evaluation:** To produce 480 units, set $ Q = 480 $: \[ 480 = 2KL \Rightarrow 240 = KL \]2. **Verification of Options:** - For $ L = 10 $, $ K = 24 $: \[ 10 \times 24 = 240 \quad (\text{Correct}) \] - For $ L = 12 $, $ K = 20 $: \[ 12 \times 20 = 240 \quad (\text{Correct}) \] - For $ L = 20 $, $ K = 12 $: \[ 20 \times 12 = 240 \quad (\text{Correct}) \] - For $ L = 24 $, $ K = 10 $: \[ 24 \times 10 = 240 \quad (\text{Correct}) \]3. **Cost Calculation:** - Cost for each option: (i) $ C = 30L + 50K $ - For

Marginal product is the change in total product due to an additional input used. Marginal product of…

Suppose that a firm's production function is given by Q = 2KL, where Q is quantity of output, K is capital, and L is units of labor. Note that MPL = K and MPK-L. The price per unit of labor and capital are $30 and $50 respectively. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 480 units of output? L = 10, K = 24 L=12, K = 20 L = 20, K = 12 L = 24. K = 10

Suppose that a firm's production function is given by Q = 2KL, where Q is quantity of output, K is capital, and L is units of labor. Note that MPL = K and MPK-L. The price per unit of labor and capital are $30 and $50 respectively. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 480 units of output? L = 10, K = 24 L=12, K = 20 L = 20, K = 12 L = 24. K = 10

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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