Question
In: Economics
4. Provide an example of utility function that describes the preferences of a consumer who consumes...
4. Provide an example of utility function that describes the preferences of a consumer who consumes only two goods and considers these two goods to be non-perfect substitutes. Explain also the meaning of variables and coefficients in the utility function.
5. Provide an example of utility function that describes the preferences of a consumer who consumes only two goods and considers these two goods to be perfect complements. Explain also the meaning of variables and coefficients in the utility function.
6. Explain precisely, what types of goods are X and Y for the consumer, whose preferences are described by utility function U(x;y) = 2x + y. Does the consumer consume X and Y always together (in what ratio?) or are X and Y perfect substitutes (substitutable at what rate?) or non-perfect substitutes for the consumer?
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...
A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?
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
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 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...
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 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.
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