3.1 Writing down the problem A firm has N inputs: G₁, G2,..., GN. The cost to rent/hire the i'th input (G) is p. The firm has a multi-input Cobb-Douglas production function, where the exponent of the i'th input is - Y=A-IN (G) = A×G × GP G The price of output is p. So, if the firm makes Y units of output, their revenue would be pY. The firm has to pay for all inputs, however, all inputs except for G₁ are fixed. This means the firm only chooses G₁. Write down the firm's profit maximization problem. 3.2 Finding the optimal level of input 1. Solve the problem you just formulated analytically. SCIENT 3. Would there be an optimal choice if >1? eco 2. Solve the problem you just formulated by "brute-force" at y₁ = 0.36, A = 1, G₁ = 1 for all i> 1, pi 0.05, p 1. Use MATLAB to evaluate profit along a grid of 100 G₁ choices and find the peak profit level. Use MATLAB to visualize the results. 3.3 Elasticity What is the elasticity of Y with respect to G₁, i.e., the sensitivity of output to input. G₁?

3.1 Writing down the problem A firm has N inputs: G₁, G2,..., GN. The cost to rent/hire the i'th input (G) is p. The firm has a multi-input Cobb-Douglas production function, where the exponent of the i'th input is - Y=A-IN (G) = A×G × GP G The price of output is p. So, if the firm makes Y units of output, their revenue would be pY. The firm has to pay for all inputs, however, all inputs except for G₁ are fixed. This means the firm only chooses G₁. Write down the firm's profit maximization problem. 3.2 Finding the optimal level of input 1. Solve the problem you just formulated analytically. SCIENT 3. Would there be an optimal choice if >1? eco 2. Solve the problem you just formulated by "brute-force" at y₁ = 0.36, A = 1, G₁ = 1 for all i> 1, pi 0.05, p 1. Use MATLAB to evaluate profit along a grid of 100 G₁ choices and find the peak profit level. Use MATLAB to visualize the results. 3.3 Elasticity What is the elasticity of Y with respect to G₁, i.e., the sensitivity of output to input. G₁?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Given: Qd = 800 - 4P Qs = 8P - 400 What is the Arc Elasticity where P = 150 and P = 100?
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elasticity at point C ?
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When is use of the arc elasticity concept valid as compared with the use of the point elasticity concept?