Question

1. Robinson Crusoe can produce two goods, X and Y, using the following production technologies:

? = 5√?_{?} and ? = 6?_{?}

His preferences over the two goods can be expressed by his
utility function ?(?, ?) = ??^{2} and he is only willing to
work a total of 6 hours in a day.

a. [4] Derive the equation of his production possibilities frontier (express the quantity of good Y as a function of good X).

b. [4] Solve for his utility maximizing consumption bundle.

c. [2] What is the implicit price ratio that he faces? (Hint: Find the price ratio that is equal to his MRS)

Answer #1

Tamer derives utility from goods X and Y, according to
the following utility function: U(X,Y)= 3 X radical y . His budget
is $90 per period, the price of X is PX=$2, and the
price of Y is PY=$6.
1. Graph the indifference curve when U=
36
2. What is the Tamer’s MRS between goods X
and Y at the bundle (X=8 and Y=2 )? What does the value of MRS
means? (أحسب القيمة واكتب بالكلمات ماذا تعني القيمة)
3....

Consider the following utility functions over goods X and Y for
two individuals:
Daves utility function : Ud(x,y) = 6min(x,y)
Jess's Utility function is Uj (x,y) = 6x + 3Y
Draw Daves indifference curve map for two specific utility
levels: U= 6 and U = 12
Draw Jess indifference curve map for two seperate utility
levels: U=6 and U=12
Explain the preferences between the two
What is the MRS for Dave? and for Jess?

) A consumer's utility function is given by: U(x,y) = 10xy
Currently, the prices of goods x and y are $3 and $5, respectively,
and the consumer's income is $150
. a. Find the MRS for this consumer for any given bundle
(x,y)
. b. Find the optimal consumption bundle for this consumer.
c. Suppose the price of good x doubles. How much income is
required so that the Econ 201 Beomsoo Kim Spring 2018 consumer is
able to purchase...

An agent has preferences for goods X and Y represented by the
utility function U(X,Y) = X +3Y
the price of good X is Px= 20, the price of good Y is
Py= 40, and her income isI = 400
Choose the quantities of X and Y which, for the given prices and
income, maximize her utility.

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)...

A consumer derives utility from good X and Y according to the
following utility function:
U(X, Y) = X^(3/4)Y^(1/4) The price of good X is $15 while good Y is
priced $10. The consumer’s budget is $160. What is the utility
maximizing bundle for the consumer?
.

George has preferences of goods 1 (denoted by x) and 2 (denoted
by y) represented by the utility function u(x,y)= (x^2)+y:
a. Write an expression for marginal utility for good 1. Does he
like good 1 and why?
b. Write an expression for George’s marginal rate of
substitution at any point. Do his preferences exhibit a diminishing
marginal rate of substitution?
c. Suppose George was at the point (10,10) and Pete offered to
give him 2 units of good 2...

1. Tina can produce any of the following combinations of
goods X and Y: (a) 100X and 0Y, (b) 50X and 25Y, and (c) 0X and
50Y. David can produce any of the following combinations of goods X
and Y: (a) 50X and 0Y, (b) 25X and 40Y, and (c) 0X and 80Y. Who has
a comparative advantage in the production of good X? Of good Y?
Explain your answer.
2. What condition must hold for the production
possibilities frontier...

1. Suppose utility for a consumer over food(x) and clothing(y)
is represented by u(x,y) = 915xy. Find the optimal values of x and
y as a function of the prices px and py with an income level m. px
and py are the prices of good x and y respectively.
2. Consider a utility function that represents preferences:
u(x,y) = min{80x,40y} Find the optimal values of x and y as a
function of the prices px and py with an...

3. Suppose that a consumer has a utility function given by
U(X,Y) = X^.5Y^.5 . Consider the following bundles of goods: A =
(9, 4), B = (16, 16), C = (1, 36).
a. Calculate the consumer’s utility level for each bundle of
goods.
b. Specify the preference ordering for the bundles using the
“strictly preferred to” symbol and the “indifferent to” symbol.
c. Now, take the natural log of the utility function. Calculate
the new utility level provided by...

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