The Se ond welrare neore n states that: a) A Walrasian equilibrium will be Pareto-inefficient, unless an “invisible hand" intervenes forcing consumers to choose a particular consumption bundle. b) A Walrasian Pareto-efficient equilibrium can be achieved as a competitive equilibrium. c) Budget constraints do not have to be always binding. d) A competitive equilibrium would be inconsistent with the concept of Walrasian equilibrium.
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- In economics, we have learned that related goods’ price does matter. Given the budget constraint and everything else remains the same, an individual consumer switches to relatively cheaper goods (also known as substitution effect). Often when you visit a chemist shop with your doctor’s prescription, your pharmacist may ask whether you are interested in buying a relatively cheaper drug (which is biologically equivalent to your prescribed drug) if it is available. what seems to be a problem that may arise when one switches to a cheaper drug.Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…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.
- Pedro, 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?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.
- 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?Extend the model of the jungle to the case in which the number of houses is smaller than the number of agents. In this case, an allocation is a function from the set of agents to the set H U {homeless} with the property that no two agents are assigned to the same house. Each agent has a preference ordering over H U {homeless}. Assume that this ordering is strict; assume also that every agent prefers to be allocated any house than to be homeless. Define an equilibrium for this extended model and show that it always exists.Assuming the two good case. When a person is attempting to maximize utility and the price of one of the two goods increases, then: The budget constraint will contract (rotate towards the origin), shifting the budget line inward indicating more choices are now affordable and a lower utility level is now possible. The budget constraint will contract (rotate towards the origin), shifting the budget line outward indicating fewer more are now affordable and a higher utility level is now possible. The budget constraint will contract (rotate towards the origin), shifting the budget line inward indicating fewer choices are now affordable and a lower utility level is now possible.
- True/False (1) If the assumptions of the first theorem of welfare economics apply and if the economy is in a competitive equilibrium, then any reallocation that benefits someone must harm someone else.< (2) The second welfare theorem of economics states that if preferences are convex, then any Pareto optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial endowments.<Suppose Vijay has 10 onion rings and 5 sheek kababs, and his friend Tara has 5 onion rings and 10 sheek kababs. Both can benefit from trade, and after trading Vijay has 12 onion rings and 3 sheek kababs. In an Edgeworth box, label the initial allocation A and the new allocation B. Draw indifference curves that are consistent with this trade being optimal for both Vijay and Tara. Put sheek kababs on vertical axis and onion rings on horizontal axis. Put Vijay on the southwest corner and Tara on northeast corner.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.