3 Consider a two period consumption saving problem. Let cı and ez denote the first and second periodsconsumption. Let the consumer incomes in periods 1 and 2 be I = $100 and I2 = $200. Assume thatthe consumer utility function is quasi-linear, u (c1, c2) = ln c + c2. Let the rate of interest r= 0.1.3.a What is the optimal consumption stream (i.e., consumption bundle)? Is the consumer a borrower or alender?3.b What will be the effect of an increase in the first period income to I = $150 on the consumption stream3.c What will be the effect of an increase in the rate of interest to r' = 0.2 on the consumption stream?What is the substitution effect and what is the income effect of the increase in the rate of interest?

U = ln c1 + c2 r = 0.10 I1 = 100 I2 = 200 Lets consider Budget line asc1 + c21+r = I1 + I21+r

Answered: 3 Consider a two period consumption…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Mary has income of $2000 today and $1000 tomorrow. She can lend and borrow at an interest rate of 20%. There is 10% inflation. Her preferences for intertemporal consumption are represented by the following utility function u(c, c) = min{c1, 2c2} (a) What is her optimal consumption bundle?
In an intertemporal optimizing model consumption, a consumer living from time zero (0) to time t has a longer utility: U (C)= ln C. The market interest rate is r and the consumer is assuming no inheritance. Derive the consumption relationship and the marginal utilities between two adjacent periods. Using a diagram, explain the time profiles of paths based on (i) above. Show that consumption is proportional to the present value of future income at time zero (0) at a given interest rate.
The production function for a company is P = 300x 0.75 0.25, where P is the amount produced given x labor and y units of equipment. Each unit of labor costs $900 and each unit of equipment costs $350. A the goal of the company is to minimize cost given a fixed production goal of 9000 units produced, what meaning of the Lagrange multiplier >? The production function for a company is P = 300x0.75 0.25, where P is the amount produced given x labor and y units of equipment. Each unit of labor costs $900 and each unit of equipment costs $350. A the goal of the company is to maximize production given a fixed budget of $50,000, what is the meaning Lagrange multiplier /?
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If you draw the cash flows from any investment, you would have negative cash flows at the beginning, and then you would receive a stream of positive cash flows thereafter. So why do we need the separate concept of a J-curve? In other words, what is the difference between a J-curve and the cash profile of any other investment?
1) In the IS equation why wasnt G in the calculations. 2)Suppose that with all exogenous variables, including T and M at their original values, households become less confident about the future and reduce their autonomous level of consumption from 200 to 150. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached. 3)Suppose that with all exogenous variables at their original values, the autonomous part of money demand increases to 70. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached.
Suppose that the least amount of goods and services that Jim will consume in a year is $40,000. Jim tends to save $0.30 of every dollar of disposable income that he makes. Use the given line to graph Jim's consumption function for disposable income levels between $0 and $200,000. Move each endpoint to the appropriate spot on the graph.
Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes).
For an economy where: C= 75 + 0.7Y |= 125 a) Solve for Y". Include your calculations. b) Draw the AE-Y graph for the economy. Include the intercept and slope of the AE function. c) On your graph from part (b), demonstrate the change that would occur if businesses increase their investment due to a change in interest rates.
Consider the problem of an individual that has Y dollars to spend on consuming over wo periods. Let c1 denote the amount of consumption that the individual would like co purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase ci units of the consumption good at a price P and can save any unspent wealth. Use s1 to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the ndividual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2.
Consider a two-period consumption saving model and let ci and c2 denote the first and second period consumption, respectively. Assume that the interest rate at which the consumer may lend or borrow is 10%. Suppose that a consumer's utility function is u (C1, c2) = c1 + 20 c2. The consumer first period income is I1 = $100 and the present value of her income stream is $330. (a) What is the optimal consumption stream (consumption bundle) of this consumer? (b) Is this consumer borrower or lender? How much does she borrow or lend? (c) What is the effect of a reduction of the interest rate to 5% on the consumer's optimal first-period saving? (Make sure to take into account the effect of the decline in the interest rate on the present value of the consumer's income stream.)
Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Ct+2 Yt+2 Yt+1 (1+r) (1+r)² (1 + r)² Ct + Ct+1 (1 + r) + 2+...+ Ct+T+1 (1+r)² \ T = Yt + + +...+ Yt+T+1 (1+r)

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