3. (a) If each consumer's utility function is continuous, strongly increasing, and strictly quasi concave on R and if the aggregate endowment of each good is strictly positive, then show that there exits one price vector, p* » 0, such that z(p*) = 0. (b) Suppose that 10 people live on a street and each of them is willing to pay $2 for each extra street light, regardless of the number of street lights provided. If the cost of providing street lights is given by C(x) = x², what is the Pareto efficient number of street lights to provide?

3. (a) If each consumer's utility function is continuous, strongly increasing, and strictly quasi concave on R and if the aggregate endowment of each good is strictly positive, then show that there exits one price vector, p* » 0, such that z(p*) = 0. (b) Suppose that 10 people live on a street and each of them is willing to pay $2 for each extra street light, regardless of the number of street lights provided. If the cost of providing street lights is given by C(x) = x², what is the Pareto efficient number of street lights to provide?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. General Equilibrium Consider a market with two goods, x and z, and two consumers, A and B. The utility functions for consumers A and B are as follows UA ÜB 2 1 == XBZB and the initial endowments for each consumer are @ eA = (4,2) еB = (2,6) where consumer B is endowed with 2 unit of good x and 6 units of good z, respectively. a) Draw the Edgeworth Box (Don't worry about the shape of the utility curves. Just pick a general shape that we have used before). b) Derive the contract curve.
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5.18 In a two-good, two-consumer economy, utility functions are u¹ (x₁, x₂) = x₁(x₂)², u² (x₁, x₂) = (x₁)²x₂. Total endowments are (10, 20). (a) A social planner wants to allocate goods to maximise consumer 1's utility while holding con- sumer 2's utility at u² = 8000/27. Find the assignment of goods to consumers that solves the planner's problem and show that the solution is Pareto efficient. (b) Suppose, instead, that the planner just divides the endowments so that e¹ = (10, 0) and e² = (0, 20) and then lets the consumers transact through perfectly competitive markets. Find the Walrasian equilibrium and show that the WEAs are the same as the solution in part (a).
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Suppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.
6) A consumer of two goods, good 1 and good 2 has a utility function u (X1, X2)= X1 0,6. X2 0,4, where x1 denotes units of good 1 and X2 units of good 2. The price of good 1 is 5 euros per unit, the price of good 2 is 3 euros per unit and the consumer's income is 150 euros. Suppose only change the price of good 1 And that the new price is p, = 2. Then the Slutsky substitution effect with respect to good 1 is Choose one: A) 8.8 B) 9.8 C) Not defined D) 7.8 E) 10.8