Consider an economy with 2 goods and 2 agents. The first agent has the utilityfunction, u (x1, x2 ) = ln x₁ + 2 ln x2, and the other one has u (y1, y2) = 2 ln yı + ln; Y2.The aggregate endowments of the 2 goods are given by (50, 100). Suppose there is asocial planner who cares about agents equally.(a)(b)Set up the planner's problem.Calculate the first-best outcome (i.e., the social planner's solution).

In this economic scenario, we have a simple economy with two goods and two agents, each with…

Answered: Consider an economy with 2 goods and 2…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider an economy with 2 goods and 2 agents. The Örst agent has the utilityfunction, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is asocial planner who cares about agents equally.(a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).
Suppose the utility possibility frontier for two individuals is given by U_a+2U_b=200 Please plot the utility frontier on a graph.
Suppose that David and his friend Wilson derive utility from consuming two types of snacks: onion rings (9₁) and chips (9₂). The utility function for each individual is U (9₁, 92) = 9192. Their indifference curves for these two goods are assumed to have the usual (convex) shape. Suppose David has an initial endowment of 35 onion rings and 10 chips, and Wilson's initial endowment consists of 5 onion rings and 20 chips. (1) Draw an Edgeworth box and show the initial allocation of goods, to be labelled e. Indicate the initial quantities of each person's goods on the four axes.
3. Christina loves pizza and hates burger. Her utility function is U(p – b) = p – 6", where is the number of pizzas she consumes and b is the number of burgers she consumes. John likes both pizza and burger. His utility function is U(p, b) = p + 2\b Christina has an initial endowment of no pizzas and 8 burgers. John has an initial endowment of 16 pizzas and 8 burgers. a. Graph the initial endowment and label it E b. If Christina hates burgers and John likes them, how many burgers can Christina and John be consuming at a Pareto optimal allocation? What is John's marginal utility for pizzas and burgers? Mark the locus of Pareto optimal allocations of pizzas and burgers between Christina and John on the grapsh above.
A and B consume only two goods, cider (C) and dumplings (D). A has an initial endowment of 10 bottles of C and 30 of D. Bob has an initial endowment of 50 bottles of cider and 50 dumplings. Alice’s utility function is uA(CA,DA) = 9ln(CA) + 10ln(DA), where CA and DA represent consumption of C and D, respectively. B’s utility function is uB(CB,DB) = CBXDB, where CB and DB denote B's consumption of C and D. a) Find the competitive equilibrium, i.e. the price ratio, of this exchange economy and the resulting equilibrium allocation. b) Find the expression of the contract curve for this economy and use your answer to check that the equilibrium allocation you found in (b) is indeed Pareto optimal.
Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3
Problem 1 Last week, neither Alistair nor Bodana purchased blueberries (x). Both consumers had $30 to spend on blueberries and/or raspberries (y), the price of the two fruits was $3 per pack and both consumers bought raspberries only. Alistair's utility for blueberries and raspberries is UA(x,y) = x+2y. Bodana's utility for blueberries and raspberries is UB(x,y) = x +12ln(y). a) In two separate graphs, illustrate Alistair's and Bodana's optimal choices. Your graphs must illustrate the consumers' budget constraints and their indifference curves at the optimal bundle. b) At their optimal bundle, what is Alistair's marginal rate of substitution of raspberries for blueberries (- MUx/MUy)? At their optimal bundle, what is Bodana's marginal rate of substitution? This week, blueberries cost $3 per pack just like last week, however raspberries now cost $4 per pack. c) How many packs of blueberries and raspberries will Alistair buy this week? Clearly justify your answer. d) Using the…
Matthew Hamming is stranded on an island. He has decided that he will spend exactly 10 hours a day gathering food. He can either spend this time gathering coconuts or catching fish. He can catch 2 fish per hour and he can gather 3 coconuts per hour. Matthew's utility function is U(FC) = 3F0.60.3 a. How many fish should Matthew catch and how many coconuts should he gather so that his consumption maximizes his utility? Illustrate the equilibrium with a graph b. One day a native inhabitant of another island arrives on the island. The visitor offers Matthew trade of 3 fish for 1 coconut. The trade fee costs 1 fish (that must be paid prior to the exchange). Will Matthew decide to trade? What will Matthew produce and consume? Justify your answer and provide a graph.
Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.
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? %3D
D2)
2

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