Question 2: Consider a competitive exchange economy with two individuals (A and B)and two goods (F and W). The total endowments of F and W are 10 each. ConsumerA has the following utility function:UA = FWwhile consumer B has preferences such that she must have one unit of F for every unitof W.(a) Derive an expression for the contract curve and illustrate in an Edgeworth box dia-gram.(b) What is the relative price of F, PF/Pw, in a competitive equilibrium?(c) Now suppose that consumer B's utility function isUB = F +2WLet consumer A's utility function remain unchanged. Derive an expression for the con-tract curve now and illustrate in a new Edgeworth box diagram.(d) What is the relative price of F, Pr/Pw, in a competitive equilibrium?

The objective of the question is to derive the contract curve and determine the relative price of…

Answered: Question 2: Consider a competitive…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Fall 2023/24) Adrienne and Stephen consume pizza, Z, and cola, C. Adrienne's utility function is and Stephen's is Us = (23) 05 (₂) 05 Their endowments are ZA-10, CA = 60, Zg=10, and C=140. What are the competitive equilibrium prices, where one price is normalized to equal one? is S $$ (Enter) UA =ZA CA Determine p, the competitive price of Z, where the price of C is normalized to equal one. Enter your response rounded to two decimal places) The competitive price, p.
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Consider the following pure exchange, Edgeworth box economy. There are two consumers, Adam and Mark, and two goods. Adam has an endowment of 7 units of good 1 and 3 units of good 2 (i.e. wadam = (7, 3)), while Mark has an endowment of 3 units of good 1 and 7 units of good2 (wmark$ = (3,7)). The consumers' utility functions are given by: Uadam = Xa1 + Xa2 and Umark = min{xm1, Xm2) where x¡1 is the consumption of good 1 by consumer (i = adam, mark) (a) Find the set of Pareto optimal allocations of this economy (b) Find the Walrasian equilibrium.
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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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6. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (b) Suppose MRSa = Ya/Xa, MRSb = Yb/Xb, Xa = 10, Ya, = 100, Xb= 50, Yb = 20, and let good Y be the numeraire (Py = 1). Verify that the competitive equilibrium price is Px = 2.
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Consider an Edgeworth box economy, where preferences and endowments are given by. ( attached below ) In the following, use the normalization p2 = 1.(a) Find all the Pareto optimal allocations (use x1 to parameterize thePO allocations). (b) Suppose the government wants individual 1 to have the bundle x1 = (5, 9). Show whether the government can induce this outcome an equilib- rium with transfers. Find the supporting prices and transfers if possible. (c) State the Second Fundamental Theorem of Welfare and explain how the result in part (b) relates to that theorem. (d) Suppose the government does not care what bundle individual 1 gets and only wants to ensure that the individual 1 receives utility level equal to 45. Show whether this can be achieved as an equilibrium with transfers. Find the supporting prices and transfers if possible.

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