Question

utility function over consumption today (c1) and consumption tomorrow (c2): U(c1, c2) = log(c1) + blog(c2)...

utility function over consumption today (c1) and consumption tomorrow (c2):

U(c1, c2) = log(c1) + blog(c2) where 0 < b < 1 and log denotes the natural logarithm

Let p1 denote the price of c1 and p2 denote the price of c2. Assume that income is Y. Derive Marshallian demand functions for consumption today (c1) and consumption tomorrow (c2). What happens to c1 and c2 as b approaches 0? {Math hint: if y = log(x), dy/dx = 1/x}

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a consumer with preferences over current and future consumption given by U (c1, c2) =...
Consider a consumer with preferences over current and future consumption given by U (c1, c2) = c1c2 where c1 denotes the amount consumed in period 1 and c2 the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is m1 = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p1 = p2 = 1 and let r denote the interest rate. 1. Find...
Consider a consumer with preferences over current and future consumption given by U (c1, c2) =...
Consider a consumer with preferences over current and future consumption given by U (c1, c2) = c1c2 where c1 denotes the amount consumed in period 1 and c2 the amount consumed in period 2. Suppose that period 1 income expressed in units of good 1 is m1 = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p1 = p2 = 1 and let r denote the interest rate. 1. Find...
Vanessa’s utility function is U(c1, c2) = c1/21 + 0.83c1/22, where c1 is her consumption in...
Vanessa’s utility function is U(c1, c2) = c1/21 + 0.83c1/22, where c1 is her consumption in period 1 and c2 is her consumption in period 2. In period 2, her income is 4 times as large as her income in period 1. At what interest rate will she choose to consume the same amount in period 2 as in period 1? (Choose the closest answer.)
(Intertemporal Choice )Consider a consumer whose preferences over consumption today and consumption tomorrow are represented by...
(Intertemporal Choice )Consider a consumer whose preferences over consumption today and consumption tomorrow are represented by the utility function U(c1,c2)=lnc1 +?lnc2, where c1 and c2 and consumption today and tomorrow, respectively, and ? is the discounting factor. The consumer earns income y1 in the first period, and y2 in the second period. The interest rate in this economy is r, and both borrowers and savers face the same interest rate. (a) (1 point) Write down the intertemporal budget constraint of...
A consumer’s consumption-utility function for a two-period horizon (t = 1, 2) is given by U(c1,c2)...
A consumer’s consumption-utility function for a two-period horizon (t = 1, 2) is given by U(c1,c2) = ln(c1)+ln(c2). The consumer’s income stream is y1 = $1500 and y2 = $1080, and the market rate of interest is 8%. Calculate the optimal values for c1 and c2 that maximize the consumer’s utility
Hira has the utility function U(c1; c2) = c11/2 +2c21/2 where c1 is her consumption in...
Hira has the utility function U(c1; c2) = c11/2 +2c21/2 where c1 is her consumption in period 1 and c2 is her consumption in period 2. She will earn 100 units in period 1 and 100 units in period 2. She can borrow or lend at an interest rate of 10%. Write an equation that describes Hira’s budget. What is the MRS for the utility function between c1 and c2? Now assume that she can save at the interest rate...
Maximise the utility u=5*ln(x-1)+ln(y-1) by choosing the consumption bundle (x,y) subject to the budget constraint x+y=10....
Maximise the utility u=5*ln(x-1)+ln(y-1) by choosing the consumption bundle (x,y) subject to the budget constraint x+y=10. Here, ln denotes the natural logarithm, * multiplication, / division, + addition, - subtraction. Ignore the nonnegativity constraints x,y>=0. Write the quantity x in the utility-maximising consumption bundle (x,y). Write the answer as a number in decimal notation with at least two digits after the decimal point. No fractions, spaces or other symbols.
Tom has preferences over consumption and leisure of the following form: U = ln(c1)+ 2 ln(l)+βln(c2),...
Tom has preferences over consumption and leisure of the following form: U = ln(c1)+ 2 ln(l)+βln(c2), where ct denotes the stream of consumption in period t and l, hours of leisure. He can choose to work only when he is young. If he works an hour, he can earn 10 dollars (he can work up to 100 hours). He can also use savings to smooth consumption over time, and if he saves, he will earn an interest rate of 10%...
A consumer likes two goods; good 1 and good 2. the consumer’s preferences are described the...
A consumer likes two goods; good 1 and good 2. the consumer’s preferences are described the by the cobb-douglass utility function U = (c1,c2) = c1α,c21-α Where c1 denotes consumption of good 1, c2 denotes consumption of good 2, and parameter α lies between zero and one; 1>α>0. Let I denote consumer’s income, let p1 denotes the price of good 1, and p2 denotes the price of good 2. Then the consumer can be viewed as choosing c1 and c2...
Let L denote the set of simple lotteries over the set of outcomes C = {c1,c2,c3,c4}....
Let L denote the set of simple lotteries over the set of outcomes C = {c1,c2,c3,c4}. Consider the von Neumann-Morgenstern utility function U : L → R defined by U(p1,p2,p3,p4)=p2u2 +p3u3 +4p4, where ui,i = 2,3, is the utility of the lottery which gives outcomes ci, with certainty. Suppose that the lottery L1 = (0, 1/2, 1/2,0) is indifferent to L2 = (1/2,0,0, 1/2) and that L3 = (0, 1/3, 1/3, 1/3) is indifferent to L4 = (0, 1/6, 5/6,0)....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT