6 [Taken from MWG 19.C.4] Consider an exchange economy with a single consumption good, twostates, and two consumers. Each consumer's preferences are represented byu" (x*) = nx + Txandu" (x*) = 7 log x} + n log x²,where x, is the amount of good consumed in state s by consumer i, and 7 is the subjective prob-ability of consumer i for state s. Since consumer a's (b's) Bernoulli utility function is assumedlinear (concave), a is risk-neutral (risk-averse, respectively). The total endowments of this econ-omy also depends on the state: w = (w,w2). Assume that each consumer is endowed with itshalf: w" = w = }(wr,w2).(a) Suppose that the two consumer share the same belief about the states:nf = n = T1T = n = 12.andShow that at an interior Arrow-Debreu equilibrium consumer b insures completely.(b) Suppose that the two consumers have different beliefs about the states. Show that at aninterior equilibrium consumer b will not insure completely. Which is the direction of thebias in terms of the differences in subjective probabilities? Argue also that consumer a willnot gain from trade.

According to the economic theory, the "Arrow-Debreu equilibrium," all markets in an economy work…

(a) Suppose that the two consumer share the same belief about the states: 7₁ = 7² = 7₁ and 7² = 7² = 7₂. Show that at an interior Arrow-Debreu equilibrium consumer b insures completely. (b) Suppose that the two consumers have different beliefs about the states. Show that at an interior equilibrium consumer b will not insure completely. Which is the direction of the bias in terms of the differences in subjective probabilities? Argue also that consumer a will not gain from trade.

(a) Suppose that the two consumer share the same belief about the states: 7₁ = 7² = 7₁ and 7² = 7² = 7₂. Show that at an interior Arrow-Debreu equilibrium consumer b insures completely. (b) Suppose that the two consumers have different beliefs about the states. Show that at an interior equilibrium consumer b will not insure completely. Which is the direction of the bias in terms of the differences in subjective probabilities? Argue also that consumer a will not gain from trade.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.1P

See similar textbooks

Similar questions

Page < 2 Question 1: Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B. There are 20 units of X and 20 units of Y in the economy. The preferences of the consumers are represented by the following utility functions: UA(XA, YA) = 4XA + 3YA of 3 UB (XB, YB) = 5(XB)4 (YB)² Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer B has 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Pybe the prices of goods X and Y, respectively. Write down expressions for the two individuals' budget constraints.
Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U = 4P + 3C . In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of Pepsi
H7. Consider an economy consisting of two consumers, Adam and Eve. There are two goods, apples and bananas. Adam likes apples and prefers more apples to less. He somewhat likes bananas: he prefers one banana to none, but is indifferent between having one banana and having more than one banana (i.e., he gets satiated with bananas after having one banana). Eve likes bananas and prefers more bananas to less; she is indifferent to apples. There are exactly 5 apples and 4 bananas available in this economy. Describe all Pareto optimal allocations in this economy. Explain.
Catherine wins a non-transferable, non-refudnable ticket to attend Saturday's baseball game. Taylor plans to attend the same game, but she knows from experience she can purchase a $40 ticket the day of the game. On the day of the game, it is cold with off-and-on rain showers, weather that both Catherine and Taylor equally dislike, making the prospect of attending the game less attractive than before. If both Catherine and Taylor have the same tastes and rational: a. Is one of them more likely to attend the baseball game than the other? b. Instead of winning a ticket, assume that last week Catherine paid $40 for the non-trasnferable, non-refundable ticket to Saturday's game. Would this change whether or not one of them is more likely to attend the baseball game?
Q. 4 Two consumers, A and B, live in a pure exchange economy with two good, x and y. Consumer A is endowed with 0 unit of x, 14 units of y; Consumer B is endowed with 4 unit of x, 6 units of y. They both have the utility function U=x1/4y3/4. What will be consumer A’s consumption of good X?
A farmer produces both green beans and corn. The farmer must give up 31 bushels of corn to get 7 more bushels of green beans. If the rate of transformation (or tradeoff) between the two goods is constant, then the opportunity cost of 1 bushel of green beans in terms of bushel of corn is? The result should be given to two decimal places in absolute value (e.g if the result is 3.678, write 3.68, if the result is -3, write 3.00.) Your Answer:
Consider a pure exchange economy with two goods and two agents, A and B. Agents A and B have the same utility u (1, y) = /TY. Since the agents' initial allocations are given by eA = (4.2) and eB = (2.4), then the Walrasian equilibrium will be composed of the following consumption baskets: %3D O (XA,YA )=(2,2) e (Xg,Ye) = (4,4) (Xa, YA)=(1,0) e (Xg,Yg)=(5,6) (XA,YA)=(2,4) e (Xg,YB)=(4,2) (XA,YA)=(3,3) e (Xg,Ye)=(3,3) o (XA,YA)=(1,1) e (Xg,YB)=(5,5)
10.3. Suppose the production possibility frontier for guns (X) and butter (Y) is given by X² + 2Y2 = 900 a. Graph this frontier. b. If individuals always prefer consumption bundles in which Y = 2X, how much X and Y will be produced? c. At the point described in part b, what will be the slope of the production possibility frontier, and what price ratio will cause production to take place at that point? (Hint: By using the approach in the numerical exam- ples in this chapter, show that the slope of this pro- duction possibility frontier is -X/2Y.) d. Show your solution on the figure from part a.
Assume the market clearing price is $5.00 for deli sandwiches and the amount of exchange that would take place at that price is 200 deli sandwiches per day. You, however, don't have this information and have just opened your deli. You decide to price your sandwiches at $9.00 and are willing and able to sell 285 sandwiches per day at that price. When you do this, you notice you sell 100 sandwiches per day. Draw this situation on a graph and then explain what will happen in this market -- i. e., if there is a shortage or surplus, show this on the graph and then explain what the shortage or surplus will cause to happen in the market. Make sure you talk about inventories in your answer.
3 Consider a pure exchange economy with 2 consumers and 2 goods. Consumer ? owns 8 units of good 1 and 1 unit of good 2, and his preference is represented by the following utility function: uA(x1, x2) = x1*x2. Consumer ? owns 2 units of good 1 and 4 units of good 2, and his preference is represented by the following utility function: uB(x1,x2)=x1+x2. Assume that the two consumers are allowed and able to trade with each other, and that good 1 is the numeraire. In this case, both consumers act as price-takers. Price takers: a market participant that is not able to dictate the prices in a market. Therefore, a price taker must accept the prevailing market price. Please find the competitive equilibrium of this pure exchange economy.
There are two goods in the economy: electricity (E) and the composite good (Y). Suppose the government subsidizes the first 20kWh of electricity consumption so that the price of electricity is ¥5 for first 20kWh and ¥10 thereafter, while the price of the composite good remains constant at py = ¥10. (a) Placing the composite good on the vertical axis and electricity on the hor- izontal axis, carefully sketch the budget set for the consumer who has income ¥500. (b) Suppose a consumer's utility function is given by u(E,Y)= EY. Find the consumer's utility maximizing bundle.
Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y). Individual A is endowed with 5 units of good X and 3 units of good Y, while individual B with 3 and 4 units of goods X and Y, respectively. Assuming utility functions of individuals A and B to be UA=XA YA² and UB-XB² YB where Xi and Yi for i= {A, B} represent individual i's consumption of good X and Y respectively, what will be the set of Pareto optimal allocation in this economy?