Chepa’s utility function is given by U (x, y) = ln x + 4 ln y.
Assume that Chepa has endowments (10, 10) and that Py = 10
throughout the problem. (h) This part of the question is to
investigate Chepa’s welfare under different prices. We will do it
step by step.
(i) By substituting out the M with the expression of Chepa’s
endowment income (see part (g)), obtain Chepa’s gross demands as
functions of Px.
(ii) Plug your answer...
Which of the following utility functions is a Cobb-Douglas?
Group of answer choices
U(x,y) = ln(x) + 4y
U(x,y) = 2x + 4y
U(x,y) = ln(x) + 4ln(y)
U(x,y) = min{x, 4y}
None of the above
Consider the utility function, U(x,y) = ln(x) + y. Please answer
the following questions, showing all work. (1) Derive an expression
showing the overall effect of an increase in py on the quantity of
y consumed, holding constant px and income (I). (2) Now, show how
that overall effect in (1) can be decomposed into a separate
substitution effect and income effect. Show these effects
explicitly. (3) Now, do the same for x: derive an expression
showing the overall effect...
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...
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...
1. Suppose Mike’s utility function is u(x,y)=2lnx +lny.
a. Derive the demand functions.
b. Is y a Normal good?
c. Is x an ordinary good?
d. 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.
e. Now, given...
Jim’s utility function is U(x, y) = xy. Jerry’s utility function
is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) =
xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility
function is U(x, y) = x/y. Pat’s utility function is U(x, y) =
-xy.
a. No two of these people have the same preferences.
b. They all have the same preferences except for Billy.
c. Jim, Jerry, and Pat all have the same...
For a demand function u (x, y) = xy, show the demand
functions for good x and good y. (Remember that
MRS = (du/dx) / (du/dy) = px / py in
the point of interest, the tangency point of budget line and
indifference curve. The budget condition is given by
pxx + pyy = m)
for u (x, y) = x1/3 y2/3
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.
1A) For a demand function u (x, y) = xy, show the demand
functions for good x and good y. (Remember that MRS = (du/dx) /
(du/dy) = px / py in the point of interest, the tangency point of
budget line and indifference curve. The budget condition is given
by pxx + pyy = m).
1B) Calculate the own-price elasticities as well as the income
elasticities of demand for goods x and y based on your results in
A)...