please answer part c,d,e here please (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 productionfunction given byC = 4√L,where C is the number of coconuts. He does not enjoy gathering coconuts, but does enjoy hisleisure time and eating coconuts. His utility function is given byu(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 manyindividuals 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 competitivemarket, given the wage rate (w). Without loss of generality, assume the price of coconuts tobe Pc = 1.Given the market wage rate (w), how much labour would a firm hire in order to maximizeits profits? Label your answer as Lp, and note that your answer must be a function of w.(c) Now consider a consumer. A consumer maximizes his/her utility (u= CR), has the endow-ment of II (think of a consumer being an owner of the firm), and also can work L hours atthe wage rate (w).How many hours would a consumer work to maximize the utility, given the wage rate (w) andthe endowment income (II)? label it as Lg, and note that your answer must be a function ofw and II.(d) Find the equilibrium wage rate (w*). To find it out, you need to find what II is in terms ofw. Then solve for w*.(e) Is the competitive equilibrium allocation Pareto optimal? Explain your answer.

Given: Production function: C=4L Utility function: u(C,R)=CR As per parts (a) and (b) The optimal…

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 hist leisure time and eating coconuts. His utility function is given by u(C, R) = CR.

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 hist leisure time and eating coconuts. His utility function is given by u(C, R) = CR.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.4P

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