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The above figure depicts the Edgeworth box for two individuals, Al and Bruce. If the endowment is at point a, and Al has no ability to bargain, the final allocation will be at point
A) a.
B) b.
C) c.
D) d.
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- Two individuals (A and B) live on an island where they consume coconuts (good x) and bananas (good y) for survival. A owns the coconut producing part of the island and B owns the banana part. Their utility functions and endowments are given by UA (TA,YA) = A+YA +min {A, YA}, UB (TB, YB) = TB +YB + min {ïß, YB}, (ww) = (0, 12) B B Assume that the price of coconuts is p and that of bananas is 1, so relative prices are denoted by p. (ww) = (10,0) A 1. What are their respective budget constraints? 2. What are their individual demand functions? (Hint: you have to consider multiple cases for the value of p) 3. The individuals trade their endowments with each other. What is the competitive equilibrium price in the market? What are their respective utilities at equilibrium?1. If a consumer's net demands are (5, -3) and her endowment is (4,4), what are her gross demands? 2. The prices are (p. Do) = (2.3), and the consumer is currently consumingTwo individuals A and B have utility functions defined over two goods, a private good 'x') and a public good, 'F. The utility function of an agent 'i' is defined by ui = 2 log xi + log F where F =FA + FB. Each agent has 200 units of private goods x, as his endowment and 1 unit of private good can be transformed into 1 public good F. Answer the following (a) Find the Nash equilibrium values of FA and FB? (b) What is the Pareto optimal level of F? (c) In what condition the Pareto optimal level of F will not depend on the number of private goods? (d) What would be the consumption of x by each agent if they contribute equally towards the public good (F)? (e) Would it change if an agent had a larger endowment of x to begin with?
- (5) A has utility function u4(x4) = x4 + x and initial endowment w4 = (3,6). Consumer B has utility function uB (xB) = xf · x% and initial endowment wB = (3,6). Consider an exchange economy with two consumers and two goods. Consumer (a) Is the initial endowment a Pareto efficient allocation? Justify your answer. (b) Find a competitive equilibrium (p, xª, x³) for the economy. (c) Construct the contract curve. A picture here is not a complete answer; you need to specify analytically the set of points that are in the contract curve.An Arrow-Debreu equilibrium occurs under the following assumption(s): (1) Consumers have a set of well-defined preferences (continuous, nonsatiated, and convex). (1I) Each consumer holds an initial endowment of the commodities, with a positive quantity of at least one commodity. (II) Production is increasing returns to scale. (iV) Production is decreasing returns to scale or constant returns to scale.: A) I and II B) I, II, and IV C) II D) Il and II 5. According to the following graph, at which point is the consumer choosing neither to borrow nor to save?:* Consumer's Budget Constraint Second-period consumptien C2 (11 + v2 Y2 Y2 First-period consumption O A) Point A OB) Point B OC) Point C OD) Point DThis question is related to equilibrium and its drive? all detail is given in a snap.
- !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.Note: The answer should be typed.
- Consider an Edgeworth box economy where preferences are given by u'lx},x3) = x} + Inx and uaf,x3) = xi, and the initial endowments are e' = (1,3) and e² = (3,1). Find all the Walrasian equilibrium. You may assume that the solution is inte- rior.(1) Consider a small exchange economy with two consumers, A and B, and two commodities, ₁ and 2. Consumer A's initial endowment is 3 units of ₁ and 2 unit of 2. Consumer B's initial endowment has 5 units of 2₁ and 4 units of r2. Consumer A's utility function is given by U(₁, ₁) = x^x^. Consumer B's utility function is given by U(x,x) = 2x² + x2. Note that and are the amounts of the two goods for Consumer A, and rf and are amounts of the two goods for Consumer B. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Consumer A's consumption from the lower left and Consumer B's from the upper right. Also measure the number of ₁ on the horizontal axis and the number of r2 on the vertical axis. (b) Draw Consumer A's indifference curve (ICA) going through E. (c) Draw Consumer B's indifference curve (ICB) going through E.!
