Question 4: Finding Contract Curve and Competitive equilibrium PriceIn a pure exchange economy with two goods, G and H, the two traders have Cobb-Douglas utilityfunctions. Suppose that Trinity's utility function is Ur = Gr Hr, and Miyoung's utility function is UM =GM (HM)². Between them, they own 100 units of G and 50 units of H.a. Solve for their contract curve.b. Determine P, the competitive price of G, where the price of H is normalized to equal one.

The economic situation does not always remain favorable for every individual in the market. The…

Question 4: Finding Contract Curve and Competitive equilibrium Price In a pure exchange economy with two goods, G and H, the two traders have Cobb-Douglas utility functions. Suppose that Trinity's utility function is U = G, H, and Miyoung's utility function is UM = GM (HM)². Between them, they own 100 units of G and 50 units of H. a. Solve for their contract curve. b. Determine P, the competitive price of G, where the price of H is normalized to equal one.

Question 4: Finding Contract Curve and Competitive equilibrium Price In a pure exchange economy with two goods, G and H, the two traders have Cobb-Douglas utility functions. Suppose that Trinity's utility function is U = G, H, and Miyoung's utility function is UM = GM (HM)². Between them, they own 100 units of G and 50 units of H. a. Solve for their contract curve. b. Determine P, the competitive price of G, where the price of H is normalized to equal one.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

5. Given that excess demands are continuous and satisfy Walras' law, use Brouwer's Fixed Point Theorem to establish the existence of competitive equilibrium in a simple exchange economy. Suppose that an apple orchard is located next to a bee keeper. If the orchard produces x apples and the bee keeper produces y honey and the cost functions of the two are as follows: C(x) = x² + 10x +9 C(y) = y² - 8x What will be the socially optimal amount of apples that can be produced? How does this compare to privately optimal amount?
Question 2: Discuss whether we can derive the Pareto set of a two-agent two-good pure exchange economy directly from agents' offer curves.
Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by UA, UB: RR where uA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient. For all price vectors PER3 we have p1z₁ + P2z2 = 0 where z; is the excess demand of good i € {1, 2}. O Preferences of both players satisfy strict convexity. At initial endowment eA= (5, 5), eg = (5, 5), there is a Walrasian Equilibrium with prices p = (1, 2).
Problem 3: Consider a pure exchange economy with two consumers (4 and B) and two goods (X and Y). Suppose consumers A and B have the utility functions: UA (XA, YA) u³ (XB, YB) = a1-a 81-8 = XBYB a. Derive the equation of the contract curve. b. Let the endowments of the economy be 1 unit of X and 2 units of Y. Show that an equal division of goods (an egalitarian outcome) is not Pareto optimal. What condition on the parameters of the utility functions is required for equal division of goods to be Pareto optimal? 0 < a < 1 0 < 3 <1 3
In an exchange economy, there are two people (Shadi and Nino) and two goods (x1 and x2). Their initial endowments are ωS = (2, 4) and ωN = (3, 6). Their utility is given by the following functions: US(x1,x2) = x12x23 and UN(x1,x2) = x1x24. Which of the following is the equation for the contract curve? Group of answer choices a. x2N = 96x1N / (15 + 4x1N) b. x2N = 47x1N / (8 + 4x1N) c. x2N = 91x1N / 5 d. x2N = 16x1N / (3 + x1N) e. x2N = 41x1N / (9 + x1N)
Consider an exchange economy with 2 agents and 2 goods. In an Edgeworth-Bowley diagram, show and illustrate that if both agents have the same preferences, the contract curve is a straight line from the bottom left-hand corner to the top right-hand corner. Does it follow that if the agents do not have the same preferences, the contract curve is not a straight line? Suppose the two agents have the same endowments and the same preferences. Is mutually beneficial trade possible? Illustrate in an Edgeworth Bowley diagram. State and explain Walras Law. What are the implications of Walras’s Law? Illustrate Walras Law in an Edgeworth-Bowley diagram.
5. Consider an exchange economy with 2 agents and 2 goods. a) In an Edgeworth-Bowley diagram, show and illustrate that if both agents have the same preferences, the contract curve is a straight line from the bottom left-hand corner to the top right-hand corner. Explain. b) Does it follow that if the agents do not have the same preferences, the contract curve is not a straight line? Explain. c) Suppose the two agents have the same endowments and the same preferences. Is mutually beneficial trade possible? Illustrate in an Edgeworth Bowley diagram. Explain.
Consider a two-agent two-good exchange economy. Assume the utility functions are given by U'(x}, x}) = x} + 4/x} and U²(x², x3) = x² + 2/x% with endowment vectors R' = (4, 12) and R? = (8, 8). Assume good x2 is the numeraire. a. Find the competitive equilibrium allocation and prices for this pure exchange economy.
Here are the questions and answers : Please draw the graphs for each answers and include all axis and details: PLEASE DO NOT SOLVE THE QUESTIONS THEY HAVE ALREADY BEEN SOLVED. Any further information needed is in the image. C) Determine the equilibrium price of good x (setting the price of good y as 1) that prevails at Home and Foreign under autarky – that is, when they do not trade with each other. Explain why any other price could not be the equilibrium price in autarky." 2 graphs one for home and one for foreign should be "Home and Foreign’s PPF" In autarky, each country has to produce both goods, otherwise, consumers would achieve a utility of 0 if one of the goods they like to consume is not available (plug 0 in one of the goods in the utility function and you get 0 level of utility). From the profit maximization problem in each industry at Home, we know that PxMP LxH = wH = PyMP LyH, At Home, the relative price of x in autarky is given by: PxMP LxH = wH = PyMP LyH…
There are two goods, Computers and Wheat, and two factors of production, capital and labor. Production in both sectors satisfies constant returns to scale. Production of computers is relatively more capital-intensive. Both input and final goods markets are competitive. Goods are freely traded internationally, but factors are immobile across countries. We will focus our analysis on the Home country. In the initial equilibrium, the Home country produces both computers and wheat, but only exports wheat. In our analysis, we will consider the following sequence of time-frames: . In the short run, both factors are completely specific to their initial sectors of employ- ment. (i.e. both factors are used to produce both goods, but in the short run it is impossible to relocate the factors that are currently in use for production) • In the medium run, capital is specific but labor can relocate. • In the long run, both factors are mobile across sectors. • In each run, the prices of factors adjust…
There are two goods, Computers and Wheat, and two factors of production, capital and labor. Production in both sectors satisfies constant returns to scale. Production of computers is relatively more capital-intensive. Both input and final goods markets are competitive. Goods are freely traded internationally, but factors are immobile across countries. We will focus our analysis on the Home country. In the initial equilibrium, the Home country produces both computers and wheat, but only exports wheat. In our analysis, we will consider the following sequence of time-frames: In the short run, both factors are completely specific to their initial sectors of employ- ment. (i.c. both factors are used to produce both goods, but in the short run it is impossible to relocate the factors that are currently in use for production) . In the medium run, capital is specific but labor can relocate. . In the long run, both factors are mobile across sectors. • In each run, the prices of factors adjust…
Consider a 2-good, 2-agent pure exchange economy where the initial endowment is eд = (5, 5), eß = (5, 5) and preferences are represented by UA, UB: R → R where UA (XA) UB (XB) = X₁X2 and Which 2 of the following 8 options are false: For all B [0, 1], the initial endowment is a Walrasian Equilibrium allocation. If B<1 then at prices p = (1,1) there will be excess demand of good 2 and excess supply of good 1. O For all B € [0, 1], every Pareto efficient allocation can be supported as a Walrasian Equilibrium for some reallocation of resources. O For any prices p = (1, 1), the budget sets of both players leave the Edgeworth box. For all B € [0, 1], the bottom left and top right corners of the Edgeworth box (0A and Og) are both Pareto efficient. For all B [0, 1], the Walrasian Equilibrium will be Pareto efficient. For all 8 [0, 1], Bob's preferences are strictly convex. For ß = 1/2, the Pareto Set is the straight line joining OA and Og.