Please correct answer and don't used hand raiting Use the Envelope Theorem to explain the meaning of the Lagrange multiplier in thefollowing equality-constrained optimization problem,max f(x), subject to g(x) = c.

Optimization Problem Setup:We are given that:maxf(x) Subject To g(x)=cHere, f(x) is the objective…

Answered: Use the Envelope Theorem to explain the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Robinson Crusoe has exactly 12 hours per day to spend gathering coconuts ( C) or catching fish (F). Let tp denote the time (in hours) spent catching fish and tc the time (in hours) spent gathering coconuts per day. Robinson can catch 3 fish per hour or he can gather 6 coconuts per hour; his "production technology" can thus be described by: F = 3tp and C = 6tc. Robinson's utility function is U(F,C) = FC where F is his consumption of fish and C is his consumption of coconuts. 1. (a) Write down Robinson's time constraint and hence find an equation for his Production Possibility Frontier (PPF). (b) Find the number of fish Robinson will catch per day and the number of coconuts he will gather per day.
Consider the following consumption problem commonly referred to as the "cake- eating" problem. The consumer starts with a certain amount of capital, ko (e.g. a certain size for the cake), and "eats" it over time. The consumer's problem is to maximize: 3* log(ct) max t=0 subject to the constraints: ki+1 > k – Ct ko 0 given > a) Write down Bellman's equation for this problem.
Don't use ai i will report you answer solve it as soon as possible with proper explanation
Review Appendix 2A of Griffin (on Lagrangian Method). Especially go over Box 2A.1. Using the utility function U = (x^1)(5w^1)(5), income = 40k, p_x = 1, find the demand function for water. (Follow the same steps.).
can you please provide a explanation with any mathematical working out
This is macroeconomics theory
Consider U(q1,q2) = q1 + v(q2) where v' > 0 and v'' < 0. This utility function is called a quasi-linear utility function. Assume q1 is a numeraire. Find the demand function for q2. *What does v mean in this question? Also, could you solve this problem without using Lagrange multipliers? Thank you.
You are working as an economic consultant and investigating the intertemporal consumption choice of clothes. Your colleague suggests using the utility function: u = min(c1, c2), where c₁ is the consumption of clothes today and C2 is the consumption of clothes tomorrow. Do you agree with your colleagues suggestions? Explain and if relevant suggest an alternative.
Given the utility function U = x₁2/5x23/5; when x₁ = 100 and x₂ = 200; choose the correct options. A Consuming one more unit of x2 delivers higher value of Utility compared with an increase of consumption of one unit of x1 B Utility function is a constant returns to scale function. The proportionate change in utility is the same as the proportionate change in each input. Utility function is an increasing function Marginal utility with respect to x1 is equal to 0.1447 when x1 = 100 and x2 = 200 E Marginal utility function is an increasing function F None of the given answers is valid
for small change in x
Paige has the utility function U(x, y) = ln(x) + 4y Do not worry about corner solutions when answering the following questions, you can use the Lagrangian multiplier method. Paige's budget constraint is px x +Pyy = I
(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…

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Use the Envelope Theorem to explain the meaning of the Lagrange multiplier in the following equality-constrained optimization problem, max f(x), subject to g(x) = c.