Question
In: Economics
Suppose both Smith and Jones utility functions of U(X,Y) = X1/2Y1/2. Smith is endowed with (X,...
Suppose both Smith and Jones utility functions of U(X,Y) = X1/2Y1/2. Smith is endowed with (X, Y) = (9,25) and Jones is endowed with (X, Y) = (25,9).
a. Draw an Edgeworth box with indifference curves through this endowment.
b. At what combinations of X and Y are both better off (i.e., are Pareto Improving)?
c. At what combinations of X and Y are there no more gains from trade (i.e., are Pareto Efficient)?
d. If they agreed on a price of one X for one Y, would they be better off?
Solutions
Rahul Sunny answered 7 months agoRelated Solutions
Imagine you consume two goods, X and Y, and your utility function is U = X1/2Y1/4....
Imagine you consume two goods, X and Y, and your utility
function is U = X1/2Y1/4. Your budget is M =
630; PX = $10; PY = $30. Now imagine PX increases to $25. The
compensated price bundle is (30.9458, 12.8941). What is the income
effect on X?
Imagine you consume two goods, X and Y, and your utility function is U = X1/2Y1/4....
Imagine you consume two goods, X and Y, and your utility function
is U = X1/2Y1/4. Your budget is M = 630; PX = $10; PY = $30. Now
imagine PX increases to $25. The compensated price bundle is
(30.9458, 12.8941). What is the income effect on X?
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.
each of the following situations, 3. U(X,Y) = X1/2Y1/2 M = $36; PY = $1; PX...
each of the following situations,
3. U(X,Y) = X1/2Y1/2 M = $36; PY = $1; PX is initially = $1; the
price of Good X increases to PX = $9.
4. U(X,Y) = X1/2Y1/2 M = $64; PY = $1; PX is initially = $16;
the price of Good X decreases to PX = $1.
1）calculate the change in the quantity demanded of Good X that
is due to the Substitution Effect
2）calculate the change in the quantity demanded of...
Suppose Mike’s utility function is u(x,y)=2lnx +lny. 1. Derive the demand functions. 2. Is y a...
Suppose Mike’s utility function is u(x,y)=2lnx +lny.
1. Derive the demand functions.
2. Is y a Normal good?
3. Is x an ordinary good?
4. Assume the price of x is initially 1 dollar, and the price of
y is also 1 dollar. Given that income is 9, if the price of x
doubles to 2 dollars, decompose the change in consumption of x into
substitution effect and income effect. Illustrate your answer with
a graph.
5. Now, given the...
Consider the utility functions of three individuals: u(x) = x1/2, v(x) = ln x, and h(x)...
Consider the utility functions of three individuals: u(x) =
x1/2, v(x) = ln x, and h(x) = x – 0.01 x2,
where x represents wealth.
Consider also the following lotteries: X = (w0 +
x1, w0 + x2, w0 +
x3; ¼, ½, ¼ ) = (4, 16, 25; ¼, ½, ¼), where
w0 = $2, and lottery Y in which w1 = $10, so
that Y = (12, 24, 33; ¼, ½, ¼). Note that Y = X +...
Consider the following utility functions: (i) u(x,y) = x2y (ii) u(x,y) = max{x,y} (iii) u(x,y) =...
Consider the following utility functions:
(i) u(x,y) = x2y
(ii) u(x,y) = max{x,y}
(iii) u(x,y) = √x + y
(a) For each example, with prices px = 2 and
py = 4 find the expenditure minimising bundle to achieve
utility level of 10.
(b) Verify, in each case, that if you use the expenditure
minimizing amount as income and face the same prices, then the
expenditure minimizing bundle will maximize your utility.
Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y, with some Px and Py...
Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y,
with some Px and Py
a. For an interior solution, solve step-by-step for the demand
functions of X* and Y*.
b. Under what circumstance would the optimal consumption involve
a corner solution for the utility maximization problem?
c. (Now, let Py = $1, I = 24, and suppose that Px increases from
$0.5 to $2. Find the Compensating Variation (CV) and the
Equivalence Variation (EV). In this example, how...
"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...
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