Question

Suppose Sophie receives utility from bananas and apples. If A = # of apples Sophie consumes and B = # of Bananas she consumes, Sophie's utility function can be described as U (A, B) = ln(A) + 2ln(B). Sophie is also able to purchase fractions of fruit instead of having to buy whole amounts.

a) Income = Y, price of apples = p(a) and price of bananas = p(b). Derive the demand for apples.

b) Say that apples only cost $1 per apple, bananas = $.50, and Sophie has a budget of $24. How many apples and bananas will Sophie consume?

c) If the price of apples increases to $2, what is the hicksian/compensated demand for apples?

Answer #1

Angela's fruit options at the convenience store are apples and
bananas. Angela's utility function over apples, A, and bananas, B,
is given by: U(A,B)=A+B a. Describe Angela's preferences over
apples and bananas and explain her optimal decision rule b. What is
the optimal bundle if price of apples is $1 a pound and the price
of bananas is $2 a pound, and she has $100 a month to spend on
apples and bananas. c. This convenience store is closing for...

Suppose that a consumer gains utility from apples and bananas
according to the utility function: U(A,B)=A^2 ×B
a)Suppose A = 2 and B = 1. What is the marginal utility of each
good?
b)For the consumer’s utility, how valuable are apples relative to
bananas? That is, what is the MRS?
c)Suppose PA = 2 and PB = 1. How valuable are apples relative to
bananas in the marketplace? That is, what is the price ratio?
d)Suppose A = 2, B...

George is making a consumption choice over apples (a) and
bananas (b). George’s preferences are represented by u (a, b)
=(2a^2)b where a > 0 and b > 0. Denote by f = (a, b) a fruit
bundle.
1. In terms of preference relations, how does George rank the
three bundles f1 = (3, 1), f2 = (1, 3), and f3 = (2, 2) relative to
each other?
2. State George’s marginal rate of substitution (MRS) function,
MRS(a, b) (where...

Evelyn eats only apples and bananas. Suppose Evelyn has the
following utility function: ?(??, ??) = ????.
a. Evelyn currently has 40 apples and 5 bananas. What is
Evelyn’s utility at this bundle? Graph the indifference curve
showing all bundles that Evelyn likes exactly as well as the bundle
(40, 5).
b. Norah offers to trade Evelyn 15 bananas if she will give her
25 apples. Would Evelyn take this trade? Explain.
c. What is the largest number of apples...

immy's utility function is U =
Apple x Banana. The price of
apples used to be $4 per unit and price of bananas $1 per unit. His
income is $160 daily. If the price of apples decreases to $2 and
the price of banana stays the same. In order to be able to just
afford his old bundle before prices change, Jimmy's would have to
have a daily income of: ______
Referring to question 10, the substitution
effect of the...

Jimmy's utility function is U =
Apple x Banana. The price of
apples used to be $4 per unit and price of bananas $1 per unit. His
income is $160 daily. If the price of apples decreases to $2 and
the price of banana stays the same.
1.In order to be able to just afford his old bundle before
prices change, Jimmy's would have to have a daily income of:
______
2.The substitution effect of the decrease in
price of...

1. Your utility function over candy, C, and bananas, B, is
U(C,B)= ln(C)+B
a) If the price of candy is $0.50 and the price of bananas is
$1.50, what is your demand for candy?
b) If the price of candy is now $1, and the price of bananas is
Pb, what is your demand for candy? (hint: it will be a function of
Pb)
c) Using the numbers from part b and an income of $5, what is
your demand...

Suppose the utility function for goods ?? and ?? is given by:
u(x, y) = x0.5 y0.5 a) Explain the difference between compensated
(Hicksian) and uncompensated (Marshallian) demand functions. b)
Calculate the uncompensated (Marshallian) demand function for ??,
and describe how the demand curve for ?? is shifted by changes in
income , and by changes in the price of the other good. c)
Calculate the total expenditure function for ??.

Olivia likes to eat both apples and bananas. At the grocery
store, each apple costs $0.20 and each banana cost $0.25. Olivia’s
utility function for apples and bananas is given by U(A, B) = 6
(AB)1/2 . If Olivia has $4 to spend on apples and bananas, how many
of each should she buy to maximize her satisfaction?
Use the tangency condition to find the
optimal amount of A to relative to B .
MUA/PA = MUB/PB
Now plug this...

Mary’s utility preference for apples in comparison to all other
goods is described by the function U(x,y) = xy, where x is the
quantity of apples she has available to consume and y is the
aggregate quantity of all other goods. Assume that Mary has 100
apples, $1,000 in cash on hand, and that a mixed bag of all other
goods and services (anything but apples) can be purchased for $1
per bag.
Calculate the numerical value of Mary’s U(x,y)...

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