4. Consider a 2x2 pure exchange economy. Agent h's demand with h E {1,2} is given by th (yh/(2p1), yh/(2p2)) where yh is the agent's income and p = (P1, P2) is the price vector. Initial endowments are e¹ = (80, 20) and e² = (20, 80). • Compute the aggregate excess demand functions for the two goods. • Define the competitive equilibrium of the economy and depict it in an Edgeworth box. Say that as a government you would like the allocation ((60,60), (40, 40)) to emerge as an

4. Consider a 2x2 pure exchange economy. Agent h's demand with h E {1,2} is given by th (yh/(2p1), yh/(2p2)) where yh is the agent's income and p = (P1, P2) is the price vector. Initial endowments are e¹ = (80, 20) and e² = (20, 80). • Compute the aggregate excess demand functions for the two goods. • Define the competitive equilibrium of the economy and depict it in an Edgeworth box. Say that as a government you would like the allocation ((60,60), (40, 40)) to emerge as an

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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8. Begin from the baseline preferences and endowments. A. Assume Yuri is wealthier than Xavier; he has an endowment of 1100 pounds for each period (E1-E2=1100). Xavier has an endowment of only 900 pounds in each period (E₁=E2=900). Note that the market supply is unchanged (1100 + 900= 1000 + 1000 = 2000). Determine the equilibrium interest rate. % r= B. Explain why the result is different from that in question 5. Write at least five sentences.
Compare two versions of the two-period depletable resource model that differ only in the treatment of marginal extraction cost. Assume that in the second version the constant marginal extraction cost is lower in the second period than the first (perhaps due to the anticipated arrival of a new, superior extraction technology). The constant marginal extraction cost is the same in both periods in the first version and is equal to the marginal extraction cost in the first period of the second version. In a dynamic efficient allocation, how would the extraction profile in the second version differ from the first? Would relatively more or less be allocated to the second period in the second version than in the first version? Would the marginal user cost be higher or lower in the second version? Why?C
Consider an exchange economy with two investors, A and B, and one physical good. Investor, i, lives for two periods, and has lifetime utility given by U(c,c) = log(c)+ Blog(c{) Be(0,1) i={4, B} where c is consumption of the good of investor i in period t= {0, 1}. Their endowments are given by y ={y°•y?} where the first component in the endowment vector denotes the investor's endowment of the physical good in period 0, and the second component denotes the investor's endowment of the good in period 1. Importantly, the physical good is non-storable. Each investor may be willing to trade some of period 0 endowment in order to enhance consumption in period 1, or vice versa. Market structure: In period 0, investors can trade in the physical good (or equivalently, trade claims to the physical good), as well as buy and sell “futures" (i.e., promises to deliver one unit of the good in period 1). In period 1, there are no more transactions except that investors execute their promises. Use values…
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
Questions 1.4 and 1.5 refer to a consumer with preferences over food (x) and clothing (y) represented by the utility function u(x, y) = xy, and whose monetary income in 2018 was I = 2. In 2018 prices were (p2018, p2018) = (1, 1), and in 2019 they are (p2019, p2019) = (4,1). hand written plz 1.4. The true consumer price index of this individual is 01 1.5 2 2.5. 1 1.5. The consumer price index of this individual calculated as a Laspeyres index is 01 1.5 2 ☑ 2.5.
3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.
Consider a two-good two-consumer exchange economy where u1 = X1Y1 and u2 = X2Y2, endowment of person 1 = (3, 4) and endowment of person 2= (2, 2). Setting the price of good Y to one (Py = 1), what is the price of good X in the competitive equilibrium? 01 0 6/5 O 3/5 O 3/2
Assume that a country is endowed with 5 units of oil reserve. There is no oil substitute available. How long the oil reserve will last if (a) the marginal willingness to pay for oil in each period is given by P = 11 - 0.46q, (b) the marginal cost of extraction of oil is constant at $4 per unit, and (c) discount rate is 3%?
Pure exchange economy with no free disposal. There is also i=,l- el = (2, 8) and ell = (8, 2) Utility function ui : R 2+R ul (xI ) = (xI,1)2+ (xI,2) 2 and ulI (xII ) = max{2XII,1 + xII,2, xII,1 + 2XII,2} Find Edgeworth-Box Solution (all kinds of allocations needed - ind. rational, pareto, weakly pareto, core)
Consider an economy where individuals live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log(C1) + 2 log(C2), where C1 and C2 are period 1 and period 2 consumption levels respectively. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in bank accounts, earning interest rate of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2. a. What is each individual’s lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period? b. Suppose that the government introduces a social security system that will take $10 from each individual in period 1, put it in a bank account, and transfer it back to…
= Part B: Suppose you are given y₁ > 0, y2 = 0, a₁ 0,r> 0. What would happen to the opportunity set if i) the first period endowment y₁ increases or ii) the market interest rate (r) decreases? You should answer this question by drawing a figure (you can use pen and paper). Be sure to define the intercepts and slope of the opportunity set in each case. Please also answer this question in general terms.
(1) Consider a small exchange economy with two consumers, A and B, and two commodities, ₁ and 2. Consumer A's initial endowment is 3 units of ₁ and 2 unit of 2. Consumer B's initial endowment has 5 units of 2₁ and 4 units of r2. Consumer A's utility function is given by U(₁, ₁) = x^x^. Consumer B's utility function is given by U(x,x) = 2x² + x2. Note that and are the amounts of the two goods for Consumer A, and rf and are amounts of the two goods for Consumer B. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Consumer A's consumption from the lower left and Consumer B's from the upper right. Also measure the number of ₁ on the horizontal axis and the number of r2 on the vertical axis. (b) Draw Consumer A's indifference curve (ICA) going through E. (c) Draw Consumer B's indifference curve (ICB) going through E.