Suppose the utility function of the two individuals in the economy is given by UA = 2XA0.5YA0.5 ; UB = XB0.5YB0.5 and X and Y are allocated equally between the two individuals. Compute for XA, YA ,XB ,YB Calculate the MRSXY of each individual Is the allocation efficient? How so?
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Suppose the utility function of the two individuals in the economy is given by UA = 2XA0.5YA0.5 ; UB = XB0.5YB0.5 and X and Y are allocated equally between the two individuals.
- Compute for XA, YA ,XB ,YB
- Calculate the MRSXY of each individual
- Is the
allocation efficient ? How so?
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- 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.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.If an allocation is already Pareto efficient and if indifference curves between the two goods have no kinks, then a. two consumers who consume both goods must have different MRS's between them, but consumers may consume the goods in different ratios. b. two consumers with the same income who consume both goods must have the same MRS, but if their incomes differ, their MRS's may differ. c. any two consumers who consume both goods must always consume them in the same ratio. d. one consumer can be made better off but always at the expense of the other. e. all consumers receive the bundle that they prefer the most among all bundles on the entire Edgeworth box.
- If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then (Select all that applies) Group of answer choices a. two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios. b. two consumers with the same income who consume both goods must have the same MRS, but if their incomes differ, their MRSs may differ. c. any two consumers who consume both goods must consume them in the same ratio. d. for any two consumers who consume both goods, neither will prefer the other consumer’s bundle to his own. e. all consumers receive the bundle that they prefer to any other bundle the economy could produce for them.Consider Gary's utility function: U(X,Y) = 5 XY, where X and Y are two goods. If the individual consumed 10 units of X and received 250 units of utility, how many units of Y must the individual consume? 5 25 0 10Mubita and Akakulubelwa live in the Liuwa national park in Westen Province of Zambia. They consume only two goods, wild fruits (W) and game meat (G). Currently Mubita consumes 10W’s and 5G’s, while Akakulubelwa consumes 3 W’s and 9 G’s. Mubita’s Marginal rate of substitution for W to G is one and Akakulubelwa’s Marginal rate of substitution is 0.5. a) If there was a competitive market for each type of goods, would these markets produce Pareto efficient allocation?
- Mubita and Akakulubelwa live in the Liuwa national park in Westen Province of Zambia. They consume only two goods, wild fruits (W) and game meat (G). Currently Mubita consumes 10W’s and 5G’s, while Akakulubelwa consumes 3 W’s and 9 G’s. Mubita’s Marginal rate of substitution for W to G is one and Akakulubelwa’s Marginal rate of substitution is 0.5. Is the allocation provided above Pareto efficient? If so, explain why. If not, show a possible Pareto efficient allocation. If there was a competitive market for each type of posters, would these markets produce Pareto efficient allocation?Roxy has 6 pencil cases and 18 notebooks. In contrast, Bratt has 18 pencil cases and 8 notebooks. Roxy's marginal rate of substitution [MRS] for notebooks is 6 and Bratt's MRS is 4.Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. Show answer with an economic perspective.Rahul's utility function is: U(x1, x2) = min{2x1 – x2, 2x2 – x1}. Priya's utility function is: U(x1, x2) = max{2x1 – x2, 2x2 – x1} Are both Priya and Rahul always better off if they get more of one of the goods? Carefully explain.
- Consider two commodities: toy cars and batteries. Each toy car takes three batteries to operate. Suppose Andy enjoys a toy car only if it moves and Andy has no other toy that needs battery. That is, one toy car and three batteries are a set of perfect complements to Andy. Task 1: Let x1 >= 0 be the quantity of toy cars and x2 >= 0 be the quantity of batteries. FindafunctionU(x1, x2)thatrepresentsthispreference. Task 2: Draw Andy's indifference curves going through bundles (2, 3), (4, 3) and (5, 5) in the commodity space in the same graph. How does Andy's preference order these 3 bundles in terms of > or ? Task 3: What mathematical expression describes the line formed by all the corners of the indifference curves?The first graph presents the utility maximizing combinations of bread and brie that Hayden chooses when the price of bread is $1.00 per loaf and the price of brie is either $4.00 or $6.00 per wheel. The second graph shows Hayden's demand curve for brie, based on those utility maximizing points. What are the specific prices and quantities of brie associated with points A and B on Hayden's demand curve? Bread (loaves) 26 16 BC2 24 BCI Brie (wheels) Price ($) Market for brie B Demand Quantity (wheels of brie)Remy and Emile consume only cheese (x,) and strawberries (x2). Remy's preferences are described by UR = min{xf, 2x5}while Emile's preferences are described by UE = xf + x5 . Remy has 8 pieces of cheese and 1 pint of strawberries while Emile has 4 pieces of cheese and 3 pints of strawberries. (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Remy on the bottom left corner and Emile on the top right corner. Indicate the total number of units of x, and x2. Label the endowment allocation. Show Remy's and Emile's indifference curves. (b) Derive the equation of the contract curve. In your graph in (a), draw the contract curve. (c) Set x1 as the numeraire, i.e., assume p, = 1 and p2 = p. Find the competitive equilibrium. Hint: For Emile to consume at a Paretoefficient allocation, what should the prices be? (d) Redraw the Edgeworth box. Indicate the equilibrium allocation, e. Draw the equilibrium budget line.
