= 5. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u¹(x4) x + 3x4 and u (x³): 4x² + x. Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xq, q = : 0, 1, 2,...), and that the firm's production technology is such that it requires 1 unit of input to produce one unit of output. = (a) Derive the Pareto set of this economy. (b) For all Pareto-efficient allocations from (a), derive a competitive equilibrium for this economy that generates these allocations.

= 5. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u¹(x4) x + 3x4 and u (x³): 4x² + x. Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xq, q = : 0, 1, 2,...), and that the firm's production technology is such that it requires 1 unit of input to produce one unit of output. = (a) Derive the Pareto set of this economy. (b) For all Pareto-efficient allocations from (a), derive a competitive equilibrium for this economy that generates these allocations.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Please answer the question fully and completely else I will rate negative, thanks! Question 3 Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm. Consumers A and B are each endowed with a unit of each good. The utility functions of each consumer are: A: 13 4 4 u (x₁‚x2 ) = lnx₁ + Inx2 B:u ₁₂ (x, ‚ x 2 ) = x, x 2 The firm B 1 A 1 1 2 produces good 2 using good 1 as an input, according to the production function f(y) = y where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm operates to maximize profit. Page 2 If P₁ and P2 determine the utility maximizing demand of consumer are the per unit prices of goods 1 and 2, . B for each good as a function of p, and P2 · If P₁ P 2 1 and are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p2. Ifp, and p2 are the per unit 1 prices of goods 1 and 2, determine the utility maximizing demand of consumer…
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Q3: Are the following utility functions quasi-linear, quasi-concave, quasi-convex, homogenous of degree 0, homogenous of degree 1? Show your working: 1) U(x,y) = min(x,y) 2) U(x,y) = (x" + yaja
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For the utility function U = Qx^0.84Qy^(1-0.84) rate between good X and good Y at Qx= 7 and Qy=19 find the trade-off
Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つつエ B N
Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3X2A; UB(X1B,X2B)=X1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (w1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (w1B,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? An amount 7 of wealth should be transferred from consumer A to consumer B. O a. O b. None of the other answers. O c. An amount 3 of wealth should be transferred from consumer A to consumer B. O d. An amount 3 of wealth should be transferred from consumer B to consumer A. e. An amount 7 of wealth should be transferred from consumer B to…
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Consider the following utility function: U = 100x.50,0.50 A consumer faces prices of P, = $2 and Py =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X an units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y 15 tv MacBook Air 80 esc DII F1 F2 F3 F4 F5 F6 F7 F8 @ #3 % 2 7 8. Q W E Y tab s lock A S F G H J Z C V N M Onteel 8 : < CO T D
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