Question 4. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 5 units of good X and 9 units of good Y. Consumer B is given an initial endowment of 3 units of good X and 7 units of good Y. Consumer A's utility function is given by: UA(X,Y)=X¹2*Y¹2 And consumer B's utility function is given by UB(X,Y)=X³4X¹4 a) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium.

Question 4. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 5 units of good X and 9 units of good Y. Consumer B is given an initial endowment of 3 units of good X and 7 units of good Y. Consumer A's utility function is given by: UA(X,Y)=X¹2*Y¹2 And consumer B's utility function is given by UB(X,Y)=X³4X¹4 a) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 5 units of good Y. Consumer B is given an initial endowment of 5 units of good X and 3 units of good Y. Consumer A's utility function is given by: UA(X,Y)= X + 4Y, and consumer B's utility function is given by UB(X,Y)= MIN (X, 2Y). If the prices are Px = 1 and Py = 3, if each consumer sells her initial endowment and buys back her optimal bundle, which of the following statements is true? Group of answer choices Both Markets are in Equilibrium There is Excess Demand in the Market for Good X = 2.4 There is Excess Demand in the Market for Good Y = 0.8 There is Excess Supply in the Market for Good Y = 1.6 There is Excess Supply in the Market for Good X = 1.6 E
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.
Consider an exchange economy with two consumers (A and B) and two goods (x1 and x2). Consumer A has an endowment of 5 units of x1 and none of x2, whereas Consumer B has an endowment of 3 units of x1 and 15 units of x2. Consumer A's utility function is given by uA=xA1xA2, and Consumer B's utility function is given by uB=min{xB1,xB2}. Both goods are traded in competitive markets. Find the competitive equilibrium price for x2, assuming p1=1.
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 consumer consumes only good A and good B. His only source of income is an initial endowment of 40 units of good A and 10 units of good B. He insists on consuming good A and good B in fixed proportions, 1 unit of good A per 1 unit of good B. He initially faces a price of $10 per unit for each fruit. The price of good A rose to $40 per unit while the price of good B stayed unchanged. After the price change, he would (a) decrease his consumption of good A by exactly 17 units. (b) decrease his consumption or good A by at least 9 units. (c) increase his consumption of good A by exactly 5 units. (d) increase his consumption of good A by exactly 9 units. (e) decrease his consumption of good B by at least 5 units.
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.
QUESTION 1 Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wt, w) = (1,2) and Bob's endowment equals (wf , w) = (1,3). Alice's utility is given by u4 (xf, xf) = 2 ln xf + In æ£ , while Bob's utility is uB(xf, x}) = ln xf + 2 ln x? . Suppose that the social planner considers it to be imperative that agent B consumes exactly one uni of good 1 and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforce transfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 would guarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2? Answer this please Select one: O a. One half unit of good 1 has to be transferred from agent A to agent B. O b. There is no endowment for which agent B would consume x = 1 and x = 4 in the corresponding competitive…
4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.
QUESTION 1 Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wf, wg) = (1,2) and Bob's endowment equals (wf, w) = (1,3). Alice's utility is given by ua(zf, x4) = 2 ln z4 + In z4, while Bob's utility is up(zf, x}) = In z? + 2 ln z}. Find the competitive (Walrasian) equilibrium prices in this pure exchange economy. Select one: O a. P1 = 5, P2 = 3 %3D O b. P1 = 3, P2 = 7 %3D O c. P1 = 7, P2 = 3 O d. Pi = 1, P = 4 Consider the same set up as in Question 1. Which of the following consumption bundles of consumer A belong to the contract curve? Select one: O a. rf = 1, xg = 1 O b. af = 2, xg = 1 O c. af = 1, x O d. af = 2, xg = 4 %3D %3D 3
Suppose there are two consumers A and B, and two goods x and y. A's utility function has the following form UA = XA - (XB)1. Which of the following is true? Consumer A's consumption of good x exhibits a negative externality. Consumer A's consumption of good x exhibits a positive externality. Consumer B's consumption of good x exhibits a negative externality. Consumer B's consumption of good x exhibits a positive externality.
Bill is the only person on an island, and he has an endowment of 20 units of coconuts (C) and 5 units of water (W). His utility function is: U(C, W) = In(C)+2 ln(W) a) Find the marginal utility of C and W. b) Find the marginal rate of substitution when Bill consumes all of his endowment.
4. Consider an exchange economy of two goods and two individuals. Consumer A has an endowment of 100 units of good 1 and 12 units of good 2 wA = (100,12), while consumer B has an endowment of 100 units of good 1 and 3 units of good 2 wB = (100, 3). The consumers' utility functions are given by: UA х,4 + Inx,A and UB x,B + 2lnx,B %3D Which of the following allocations is not efficient? a. (x,4,x24) = (100,5), (x,³, x2³) = (100,10) b. (x,4, x24) = (50,5), (x,®, x,³) = (150,10) c. (x,4, x24) = (0,4), (x,³, x,") = (200,11) d. (x,4, x24) = (100,0), (x1",x,") = (100,15) %3D