Question

utility function over consumption
today (*c _{1}*) and consumption tomorrow
(

*U(c _{1}, c_{2})
= log(c_{1}) +* b

Let *p _{1}* denote
the price of

Answer #1

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) = 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 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.)

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

(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...

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. 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), 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 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}. 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)....

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