(a) Find the optimal allocation (C", L"), in which Robinson Crusoe acts as a social planner. (b) Now consider a de-centralized economy. That is, think of this economy that consists of many individuals with the identical taste and technology. First, consider a firm's decision problem. The firm produces coconuts (C), employing workers (L). The firm hires L in a competitive market, given the wage rate (w). Without loss of generality, assume the price of coconuts to be P₂ = 1. Given the market wage rate (w), how much labour would a firm hire in order to maximize its profits? Label your answer as Lp, and note that your answer must be a function of w.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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(2) Consider a Robinson Crusoe's economy, where he has 10 hours to spend on gathering coconuts
(L), or a leisure (R). That is, L + R = 10. He can produce coconuts based on the production
function given by
C = 4√L,
where C is the number of coconuts. He does not enjoy gathering coconuts, but does enjoy his
leisure time and eating coconuts. His utility function is given by
u(C, R) = CR.
(a) Find the optimal allocation (C*, L*), in which Robinson Crusoe acts as a social planner.
(b) Now consider a de-centralized economy. That is, think of this economy that consists of many
individuals with the identical taste and technology. First, consider a firm's decision problem.
The firm produces coconuts (C), employing workers (L). The firm hires L in a competitive
market, given the wage rate (w). Without loss of generality, assume the price of coconuts to
be Pc = 1.
Given the market wage rate (w), how much labour would a firm hire in order to maximize
its profits? Label your answer as L, and note that your answer must be a function of w.
Transcribed Image Text:(2) Consider a Robinson Crusoe's economy, where he has 10 hours to spend on gathering coconuts (L), or a leisure (R). That is, L + R = 10. He can produce coconuts based on the production function given by C = 4√L, where C is the number of coconuts. He does not enjoy gathering coconuts, but does enjoy his leisure time and eating coconuts. His utility function is given by u(C, R) = CR. (a) Find the optimal allocation (C*, L*), in which Robinson Crusoe acts as a social planner. (b) Now consider a de-centralized economy. That is, think of this economy that consists of many individuals with the identical taste and technology. First, consider a firm's decision problem. The firm produces coconuts (C), employing workers (L). The firm hires L in a competitive market, given the wage rate (w). Without loss of generality, assume the price of coconuts to be Pc = 1. Given the market wage rate (w), how much labour would a firm hire in order to maximize its profits? Label your answer as L, and note that your answer must be a function of w.
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