Question
In: Economics
Consider a consumer with preferences for consumption today versus tomorrow represented by the utility function U(C,C')...
Consider a consumer with preferences for consumption today versus tomorrow represented by the utility function U(C,C') = C2/5C'3/5. Let income today is 50, income tomorrow is 20, taxes today are 10, and taxes tomorrow are 15.
A. Assume that there is a different borrowing versus lending rate, so that the lending rate is only 5% but the borrowing rate is 10%. Calculate the optimal consumption bundle. (hint: the consumer will be a saver)
B.On a (C,C') graph that is properly labeled, please show the optimal consumption bundle obtained in part (a).
C. Given the consumer still faces this 5% lending rate, but the government now faces a 10% lending rate. Assuming the government wishes to maximize the consumer's level of utility and taxes can be negative, what change would the government make? What would be the consumer's new consumption bundle given this change?
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
Consider a consumer with preferences for consumption today versus tomorrow represented by the utility function U(C,C')...
Consider a consumer with preferences for consumption today
versus tomorrow represented by the utility function U(C,C') =
C2/5C'3/5. Let income today is 50, income tomorrow is 20, taxes
today are 10, and taxes tomorrow are 15.
a) Assume that there is a different borrowing versus lending
rate, so that the lending rate is only 5% but the borrowing rate is
10%. Calculate the optimal consumption bundle. (hint: the consumer
will be a saver)
b) On a (C,C') graph that is...
Consider a consumer with preferences represented by the utility function: u(x, y) = x1/4y1/2 Suppose the...
Consider a consumer with preferences represented by the utility
function:
u(x, y) = x1/4y1/2
Suppose the consumer has income M = 10 and the prices are px=1
and Py = 2.
(a) Are goods x and y both desirable?
(b) Are there implications for the utility maximization problem
for the consumer from your finding in 1a? If so, explain in
detail.
(c) Derive the utility maximizing bundle.
Consider a consumer with preferences represented by the utility function: u(x; y) = x1/4y1/2 Suppose the...
Consider a consumer with preferences represented by the utility
function:
u(x; y) = x1/4y1/2
Suppose the consumer has income M = 10 and the prices are px = 1
and py = 2.
(a) Are goods x and y both desirable?
(b) Are there implications for the utility maximization problem
for the consumer from your finding in a? If so, explain in
detail.
A consumer has his preferences represented by the utility function U(x,y) = min {5x + 4y,...
A consumer has his preferences represented by the utility
function U(x,y) = min {5x + 4y, 4x + 7y} if x is on the horizontal
axis and y is on the vertical axis, what is the slope of his
indifference curve at the point (10,10)
a. -4/7
b. -5/4
c. -4/5
d. -7/4
e. -5/7
Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY =...
Suppose a consumer has preferences represented by the utility
function U(X,Y) = X2Y Suppose PY = 1, and the consumer has $300 to
spend. Draw the Price-Consumption Curve for this consumer for
income values PX = 1, PX = 2, and PX = 5. Your graph should
accurately draw the budget constraints for each income level and
specifically label the bundles that the consumer chooses for each
income level. Also, for each bundle that the consumer chooses, draw
the indifference...
Consider an economy where the representative consumer has a utility function u (C; L) over consumption...
Consider an economy where the representative consumer has a
utility function u (C; L) over consumption C and leisure L. Assume
preferences satisfy the standard properties we saw in class. The
consumer has an endowment of H units of time that they allocate to
leisure or labor. The consumer also receives dividends, D, from the
representative Örm. The representative consumer provides labor, Ns,
at wage rate w, and receives dividends D, from the representative
Örm. The representative Örm has a...
"Suppose a consumer has preferences represented by the utility function U(X,Y) = X(^2)Y Suppose Py =...
"Suppose a consumer has preferences represented by the utility
function U(X,Y) = X(^2)Y Suppose Py = 1, and the consumer has $360
to spend. Draw the Price-Consumption Curve for this consumer for
income values Px =1, Px = 2, and Px = 5. Your graph should
accurately draw the budget constraints for each income level and
specifically label the bundles that the consumer chooses for each
income level. Also for each bundle that the consumer chooses, draw
the indifference curve...
Suppose a consumer has preferences represented by the utility function U(X,Y) = MIN[X,2Y]. Suppose PX =...
Suppose a consumer has preferences represented by the utility
function U(X,Y) = MIN[X,2Y]. Suppose PX = 1 and PY = 2. Draw the
Income Consumption Curve for this consumer for income values M =
100, M = 200, and M = 300. Your graph should accurately draw the
budget constraints for each income level and specifically label the
bundles that the consumer chooses for each income level. Also, for
each bundle that the consumer chooses, draw the indifference curve
that...
Jo has preferences described by the utility function, U = c0.5r0.5. Where c denotes her consumption...
Jo has preferences described by the utility function, U =
c0.5r0.5. Where c denotes her consumption of carrots in ounces and
r denotes her consumption of red meat in ounces. She faces two
constraints,
1) she has an income of 1000 and the price of c is 10, while the
price of r is 20.
2) due to health concerns, the government does not allow anybody
to consume more than 80 ounces of r.
a) write down the Lagrangian and...
Consumption-Savings Consider a consumer with a lifetime utility function U = u(Ct) + βu(Ct+1) that satisfies...
Consumption-Savings Consider a consumer with a lifetime utility
function U = u(Ct) + βu(Ct+1) that satisfies all the standard
assumptions listed in the book. The period t and t + 1 budget
constraints are Ct + St = Yt Ct+1 + St+1 = Yt+1 + (1 + r)St. Now
suppose Ctis taxed at rate τ so consumers pay 1 + τ for one unit of
period t consumption.
(a) What is the optimal value of St+1? Impose this optimal value...
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