Question
In: Economics
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?
Solutions
Rahul Sunny answered 2 years 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 = XY....
Imagine you consume two goods, X and Y, and your utility
function is U = XY. Your budget is $100, the price of Good X is $4,
and the price of Good Y is $25. So, the optimal bundle for you to
consume is (12.5, 2). Now the price of good X increases to $10. The
compensated price bundle is (7.91, 3.16). What is the income effect
on X?
1. Imagine you consume two goods, K and L, and your utility function is U =...
1. Imagine you consume two goods, K and L, and your utility
function is U = K1/3L2/3. Your budget is $120; PK = $6; PL = $9.
So, the optimal bundle for you to consume is (K = 6.6667, L =
8.8889). Now, suppose the price of good K increases to $9. What is
the new optimal K for you to consume?
2. Imagine you consume two goods, K and L, and your utility
function is U = K1/3L2/3. Your...
A consumes two goods, x and y. A ’s utility function is given by u(x, y)...
A consumes two goods, x and y. A ’s utility function is given
by u(x, y) = x 1/2y 1/2
The price of x is p and the price of y is 1. A has an income
of M.
(a) Derive A ’s demand functions for x and y.
(b) Suppose M = 72 and p falls from 9 to 4. Calculate the
income and substitution effects of the price change.
(c) Calculate the compensating variation of the price
change....
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...
An individual likes to consume 2 goods X and Y . The utility function for this...
An individual likes to consume 2 goods X and Y . The utility
function for this individual is U = X+0.5Y . What
is the marginal utility of X and Y ?
The individual has an income of $90. The price of X is $10 and
the price of Y is $5. What is the optimal
consumption
bundle of this individual? Graph the
individuals optimal bundle with the budget line and indierence
curve. (answer: Infinitely many solutions).
Do the same...
Esther consumes goods X and Y, and her utility function is U(X,Y)=XY+Y For this utility function,...
Esther consumes goods X and Y, and her utility
function is
U(X,Y)=XY+Y
For this utility function,
MUX=Y
MUY=X+1
a. What is Esther's MRSXY?
Y/(X + 1)
X/Y
(X + 1)/Y
X/(Y + 1)
b. Suppose her daily income is $20, the price of X is $4
per unit, and the price of Y is $1 per unit. What is her
best choice?
Instructions: Enter
your answers as whole numbers.
X =
Y =
What is Esther's utility when her...
A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...
A consumer purchases two goods, x and y and has utility
function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x
and MUy = 3. The price of x is px = 4 and the price of y is py = 2.
The consumer has M units of income to spend on the two goods and
wishes to maximize utility, given the budget.
Draw the budget line for this consumer when M=50 and the budget
line when...
13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y)...
13. Pip consumes two goods, x and y. Pip’s utility function is
given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of
y is 1. Pip has an income of M.
(a) Derive Pip’s demand functions for x and y. [5 marks]
(b) Suppose M = 72 and p falls from 9 to 4. Calculate the income
and substitution effects of the price change. [5 marks]
(c) Calculate the compensating variation of...
Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY....
Leon consumes two goods, X and Y. His utility function is given
by U(X,Y) = 56XY. The price of X is $14 a unit; the price of Y is
$8 a unit; and Leon has $672 to spend on X and Y.
a. Provide the equation for Leon’s budget line. (Your answer for
the budget line should be in the form Y = a – bX, with specific
numerical values given for a and b.)
b. Provide the numerical value...
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