4. Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is Q=4K 0.75 0.25, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The rental rate of capital is R = $10 per unit and wage rate is W = $15. a. Write the constrained optimization problem for Miguel and Jake. b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week? c. How much will hiring these inputs cost them (Total cost)? d. Graph the isocost line, isoquant curve, and the optimal capital and labor including intercepts.

4. Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is Q=4K 0.75 0.25, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The rental rate of capital is R = $10 per unit and wage rate is W = $15. a. Write the constrained optimization problem for Miguel and Jake. b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week? c. How much will hiring these inputs cost them (Total cost)? d. Graph the isocost line, isoquant curve, and the optimal capital and labor including intercepts.

ENGR.ECONOMIC ANALYSIS

14th Edition

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

4. Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of
paper to ship to their customers. The paper plant's long-run production function is
Q=4K 0.75 0.25
"where Q is the number of reams produced, K is the quantity of capital rented,
and L is the quantity of labor hired. The rental rate of capital is R = $10 per unit and wage
rate is W $15.
a. Write the constrained optimization problem for Miguel and Jake.
b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce
1,000 reams of paper each week?
c. How much will hiring these inputs cost them (Total cost)?
d. Graph the isocost line, isoquant curve, and the optimal capital and labor including
intercepts.

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