In a two good two consumer economy, utility functions are U1(x1,x2) =x1(x2)2 and U2(x1,x2) = (x1)2 x2 The endowments of the consumers are e1 =(10,0) and e2=(0,20). Find the allocation of goods in Walrasian equilibrium.
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- Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 8 units of X and a TOTAL of 8 units of Y. The consumers' utility functions are given by: UA(X,Y) = 2X + Y UB(X,Y) = X*Y2 Which of the following allocations is Pareto Efficient? None of the other answers are Pareto Efficient. Consumer A gets 3 units of X and 8 units of Y, and Consumer B gets 5 units of X and O units of Y. Consumer A gets 4 units of X and 4 units of Y, and Consumer B gets 4 units of X and 4 units of Y. Consumer A gets 1 units of X and 4 units of Y, and Consumer B gets 7 units of X and 4 units of Y. Consumer A gets 8 units of X and 8 units of Y, and Consumer B gets 0 units of X and O units of Y.Problem 1: Suppose that in an economy there are two goods, food, F, and clothing, C, and two consumers, Anne and Bob. Anne and Bob both have the same utility function U(F,C) = FC. The marginal rate of substitution of food for clothing associated with this utility function is MRSF.C = Firms in this economy have produced 10 units of food and 10 units of clothing. Explain why an allocation where Anne gets all the food and Bob gets all the clothing does not satisfy exchange efficiency. Explain why this allocation would never happen if Anne and Bob both have to pay the market prices for food and clothing and both make optimal choices. Hints: 1: Use the definition of exchange efficiency from the class slides or textbook. 2: Optimal choices must solve MRS=price ratio.Consider an economy with 100 pieces of apple (A) and 150 pieces of banana (B) that must be completely distributed to individuals 1 and 2. The utility function of the two individuals, U1 & U2, is given by U1 (A1,B1) = 2A2 + B2 & U2 (A2,B2) = 2A2B2, respectively. With this information, recommend an efficient allocation of the two goods between the two individuals. Discuss and show the necessary solution to support your recommendation
- 10. Consumer A and B have each been given an allocation of 2 goods x and y (assume each has positive amounts of both goods). At this allocation, consumer A has an MRS of 2, while consumer B has an MRS of 1/2. Could this allocation be Pareto efficient? Explain why or why not.Carol and Bob both consume the same goods in an economy of pure exchange. Carol is initially endowed with 9 units of good 1 and 6 units of good 2. Bob is initially endowed with 18 units of good 1 and 3 units of good 2. They both have the utility function U(x₁, x₂) = = $1), what will the equilibrium price of x1/³x/3. If we set good 1 as the numeraire (so that p₁ good 2 be?1. True/False: Partial equilibrium analysis only concerns supply or demand alone, whereas general equilibrium analysis concerns supply and demand simultaneously. 2. True/False: In general equilibrium analysis, an allocation is said to be as a reasonable allocation if each consumer consumes the same bundle its value is no more than the value of the consumer's income. 3. True/False: In general equilibrium analysis, an allocation is said to be as a reasonable allocation if each consumer consumes the same bundle its value is no more than the value of the consumer's income.
- 5. Carol and Bob both consume the same goods in an economy of pure exchange. Carol is initially endowed with 9 units of good 1 and 6 units of good 2. Bob is initially endowed with 18 units of good 1 and 3 units of good 2. They both have the utility function U(x₁, x₂) = 1/3 x1³x2³. If we set good 1 as the numeraire (so that p₁ = $1), what will the equilibrium price of good 2 be?Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 9 units of X and a TOTAL of 9 units of Y. The consumers' utility functions are given by: UA(X,Y) = 3X + Y UB(X,Y) = X2 Y For Each of the following allocations, answer True if it is Pareto Efficient, and False if it is not Pareto Efficient. [ Select ] Allocation A: Consumer A gets X = 7 and Y =6; Consumer B gets X = 2 and Y = 3. [ Select ] Allocation B: Consumer A gets X = 6 and Y =7; !3! Consumer B gets X = 3 and Y = 2 %3D [ Select ] Allocation C: Consumer A gets X = 2 and Y =0; Consumer B gets X = 7 and Y = 9 [ Select ] v Allocation D: Consumer A gets X = 1 and Y =0; Consumer B gets X = 8 and Y = 9Pedro, a retired economics professor, grows lemons and oranges in his back- yard. He consumes some of these fruits, and sells some in a local farmer's market. Pedro's preferences are represented by the following utility function U(x, y) = min{x,y}. In one season he can harvest 20 pounds of lemons and 60 pounds of oranges. In the local market, price of lemons is $4 per pounds and price of oranges is $2 per pound. Pedro receives $300 income from his retirement plan per season. Question 1 Part a Find Pedro's optimal consumption bundle. Make sure to draw his budget con- straint and indifference curves to show his optimal choice. Question 1 Part b Suppose that the price of lemons rises to $5 per pound. What is Pedro's optimal consumption bundle now? Decompose the total change in demand due to a price change into a substitution effect, ordinary income effect and endowment income effect and graphically demonstrate it.
- Carol and Bob both consume the same goods in an economy of pure exchange. Carol is initially endowed with 9 units of good 1 and 6 units of good 2. Bob is initially endowed with 18 units of good 1 and 3 units of good 2. They both have the utility function U(x₁, x₂) = 1/3 2/3 x1³x2³. If we set good 1 as the numeraire (so that p. = $1), what will the equilibrium price of good 2 be?3(b)Consider the following social choice problem in the setting of consumption of two goods by two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2. Consumer 1 has utility function U; (t,g) =6+.4 In(t) + .6 In(q) (where t is the amount of tillip 1 consumes and q is the amount of quillip). Consumer 2 has utility function U; (t,q) = 8 + In (t) + In(q). The social endowment consists of 15 units of tillip and 20 units of quillip. a. Suppose that a social dictator has social welfare functional of the following form: social welfare, as afunction of (u",u") is a weighted sum with weight 2 on the lesser of u' and u' and weight 1 on the greater of the two. What will be the welfare optimum plan chosen by this social planner? b. What is the set of all feasible, Pareto efficient allocations of the consumption good for this society? %3D7) Jane has 3 liters of soft drinks and 9 sandwiches. Bob, on the other hand, has 8 liters of soft drinks and 4 sandwiches. With these endowments, Jane's marginal rate of substitution ( MRS) of soft drinks for sandwiches is 4 and Bob's MRS is equal to 2. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is, explain why. If it is not, what exchanges will make both parties better off?