3. (a) If each consumer's utility function is continuous, strongly increasing, and strictly quasi concave on R and if the aggregate endowment of each good is strictly positive, then show that there exits one price vector, p* » 0, such that z(p*) = 0. (b) Suppose that 10 people live on a street and each of them is willing to pay $2 for each extra street light, regardless of the number of street lights provided. If the cost of providing street lights is given by C(x) = x², what is the Pareto efficient number of street lights to provide?

3. (a) If each consumer's utility function is continuous, strongly increasing, and strictly quasi concave on R and if the aggregate endowment of each good is strictly positive, then show that there exits one price vector, p* » 0, such that z(p*) = 0. (b) Suppose that 10 people live on a street and each of them is willing to pay $2 for each extra street light, regardless of the number of street lights provided. If the cost of providing street lights is given by C(x) = x², what is the Pareto efficient number of street lights to provide?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fast
3. Consider the following utility function: X2 if: 1 2 u(x1, x2) X1 if: 1< x2 < 2 X2 + x1 otherwise Answer the following questions. (a) What is the Walrasian demand for this utility function?
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2. General Equilibrium Consider a market with two goods, x and z, and two consumers, A and B. The utility functions for consumers A and B are as follows UA ÜB 2 1 == XBZB and the initial endowments for each consumer are @ eA = (4,2) еB = (2,6) where consumer B is endowed with 2 unit of good x and 6 units of good z, respectively. a) Draw the Edgeworth Box (Don't worry about the shape of the utility curves. Just pick a general shape that we have used before). b) Derive the contract curve.
3. Cost of living will become more expensive fuelled by increases in food and electricity bill. Suppose the utility function for a customer in the rural area is estimated to be U=F05E0.5 where Fis the amount of food consumed and E represent electricity usage. If the consumer income is $10,000 per week and the price of food is $500 and the electricity cost $200. a) Calculate the optimal bundles when the electricity rate increases to $250 b) What is the income and substitution effect of the price increase? c) Illustrate the income and substitution effect on a well labeled diagram,
4. What kind of preferences are represented by a utility function of the form u(r1, r2) = VI1 + x2? WWhat about the utility function v(r1,r2) = 13.r, + 13.r2? %3D %3D
2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U1 = X11X 12 U = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;= (2,2) Wy= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x;= (1,2), x2= (8,4), X3= (1,4) b. Show that x makes no one worse off than the original allocation.
2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…
Zach's preferences are representable by the utility function u = 90.3927, where 9₁ and 92 denote his consumption of goods 1 and 2. (Answers to each of these questions are rounded, where required, to two decimal places.) Still assuming endowments of e₁ = 5 and e₂ = 9 and market prices p₁ = 20 and p2 = 30, what is the maximised value of Zach's utility? O Au= 6.74 O B. u = 5.39 O Cu = 5.65 O D.u = 7.56 O E. None of the above
Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have lexicographic preferences over two goods G1 and G2 - A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.¹ Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One difference to the usual setting - there are government restrictions in place so that no individual is allowed to buy more than two units of either good. Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should suffice. 1) Suppose prices are p= (P₁, P2) = (1,2). Denote the optimal choice of A and B as a= b= (b₁,b₂) respectively. Solve for a and b. (a1, a2) and