Consider the Robinson Crusoe economy, where there is only onegood in the economy that is produced by one firm, which is owned by RobinsonCrusoe. Robinson Crusoe's utility function is given by u(x, y) = x¹/³y²/³ where xdenotes the amount of consumption of the good and y denotes the amount of leisure.Suppose that there are 24 hours of time that Cruose can allocate between leisureand work. For the firm side, suppose that the production function is f(1) = √l,where I denotes the amount of labor. Let p be the price of the good, and w be thewage rate.(a) Let II be the profit of the firm. Using II, along with the notation above, writedown the budget constraint of Robinson Crusoe as a consumer.(b) Solve the consumer problem and find the demand of the good and leisure.(c) Solve the firm's profit maximization problem.(d) Let w 1. Find the equilibrium price of the good, the demand (and supply)of the good, and the amount of labor.

Profit maximization is a fundamental concept in economics and enterprise, representing the system by…

Answered: Robinson Crusoe

Business

Economics

Robinson Crusoe

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider the Robinson Crusoe economy, where there is only one
good in the economy that is produced by one firm, which is owned by Robinson
Crusoe. Robinson Crusoe's utility function is given by u(x, y) = x¹/³y²/³ where x
denotes the amount of consumption of the good and y denotes the amount of leisure.
Suppose that there are 24 hours of time that Cruose can allocate between leisure
and work. For the firm side, suppose that the production function is f(1) = √l,
where I denotes the amount of labor. Let p be the price of the good, and w be the
wage rate.
(a) Let II be the profit of the firm. Using II, along with the notation above, write
down the budget constraint of Robinson Crusoe as a consumer.
(b) Solve the consumer problem and find the demand of the good and leisure.
(c) Solve the firm's profit maximization problem.
(d) Let w 1. Find the equilibrium price of the good, the demand (and supply)
of the good, and the amount of labor.

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Step 1: Define profit maximization

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Step 2: Explain the Budget Constraint:

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Step 3: Explain the Consumer Problem

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Step 4: Explain the Firm's Profit Maximization:

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Step 5: Explain the Equilibrium with w = 1:

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