Question

- 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) function for her current endowment of apples and all other goods.
- Find ten other combinations of apples and cash that would result in the same numerical value of U(x,y) as the value found in (a).
- Graph the starting point and the other ten points found in (b)
- At the starting point (100 apples and $1000 cash) what is the value of Mary’s Marginal Rate of Substitution of apples for a composite of all other (non-apple) goods and services. Make a table in which you show the initial endowment and each of the 10 other combinations of quantities of apples and cash that you have identified as providing equivalent numerical values of Mary’s U(x,y) function, and calculate and record in your table the corresponding values of Mary’s Marginal Rate of Substitution of apples for the composite of all other goods.

Answer #1

Ron consumes two goods, X and Y. His utility function is given
by U(X,Y) = 44XY. The price of X is $11 a unit; the price of Y is
$8 a unit; and Ron has $352 to spend on X and Y.
a. Provide the equation for Ron’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...

A person spends all his/her $400 weekly income on goods, X and
Y. His/her utility function is U(X,Y)=XY.
a) What is the marginal rate of substitution (MRS) for consuming
4 units of X and 8 units of Y?
b) How much of each good would be purchased if the price of X is
4 and the price of Y is 8?

Consider a consumer whose preferences over the goods are
represented by the utility function U(x,y) = xy^2. Recall that for
this function the marginal utilities are given by MUx(x, y) = y^2
and MUy(x, y) = 2xy.
(a) What are the formulas for the indifference curves
corresponding to utility levels of u ̄ = 1, u ̄ = 4, and u ̄ = 9?
Draw these three indifference curves in one graph.
(b) What is the marginal rate of substitution...

1)Find
Marginal Utility for x and determine if it is diminishing
Marginal utility for y and determine if its diminishing
Marginal rate of Substitution of x for y (MRSxy) and
determine if its diminishing
U (x, y) = 2x2/3y1/3
U (x, y) = x3 + 4y1/4
2. Continental Long Distance Telephone service offer am optional
package for in-stare calling whereby each month the subscriber gets
the first 50 minutes of in-state calls free, the next 100 min at
$0.25/min, and...

[Utility Maximization] Mary spends her income on housing (H) and
food (F). Her utility function is given by: U(H, F) = 3HF − H + F
Suppose the price of food is $1 per unit and the price of housing
is $2 per unit. Assume her income is $9.
a) Write down Mary’s budget constraint and find the expression
for her marginal rate of substitution (MRS(HF)).
b) Assume the optimal choice of (H*,F*) is not a corner
solution. Write the...

1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21 +
2x1x2 + x22
. Al’s wife, El Einstein, has a utility function v(x1,
x2) = x2 + x1.
(a) Calculate Al’s marginal rate of substitution between
x1 and x2.
(b) What is El’s marginal rate of substitution between
x1 and x2?
(c) Do Al’s and El’s utility functions u(x1,
x2) and v(x1, x2) represent the
same preferences?
(d) Is El’s utility function a...

Consider a two-person (1 and 2) two good (X and Y) exchange
economy. The utility function of person i is given by
??=?????1−???Ui=xiaiyi1−ai
where xi and yi denote respectively person
i's the consumption amount of good X and good Y, i=1, 2.
Suppose the endowments and preference parameter of each person
in the economy are given in following table:
Endowment of X Endowment of Y
Preference Parameter (ai )
Person 1
41
32
...

purchase goldfish and other goods. My tastes are quasilinear in
goldfish, and my utility function is U(g, y) = 50 g1/2 + y, where g
is goldfish and y is other goods. The price of other goods is $1,
and the price of goldfish is $5. My income is $500. At current
prices, I purchase 25 goldfish and spend $375 on other goods.
Suppose that my income rises to $1,000. What is my new
utility-maximizing choice of g and Y?...

Consider a consumer with the following utility function: U(X,
Y ) = X1/2Y 1/2
(a) Derive the consumer’s marginal rate of substitution
(b) Calculate the derivative of the MRS with respect to
X.
(c) Is the utility function homogenous in X?
(d) Re-write the regular budget constraint as a function of PX
, X, PY , &I. In other words, solve the equation for Y .
(e) State the optimality condition that relates the marginal
rate of substi- tution to...

Claraís utility function is u (x; y) = (x + 2) (y + 1) where x
is her consumption of good x and y is her consumption of good
y.
(a) Write an equation for Claraís indi§erence curve that goes
through the point (x; y) = (2; 8).
(b) Suppose that the price of each good is $1 and Clara has an
income of $11. Can Clara achieve a utility level of at least 36
with this budget? (
c)...

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