Question

Consider a consumer with the utility function U(x, y) =2 min(3x,
5y), that is, the two goods are perfect complements in the ratio
3:5. The prices of the two goods are Px = $5 and Py = $10, and the
consumer’s income is $330. At the optimal basket, the consumer buys
_____ units of y. The utility she gets at the optimal basket is
_____ At the basket (20, 15), the MRSx,y = _____.

Answer #1

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Consider a consumer with the utility function U(x, y) = min(3x,
5y). The prices of the two goods are Px = $5 and Py = $10, and the
consumer’s income is $220. Illustrate the indifference curves then
determine and illustrate on the graph the optimum consumption
basket. Comment on the types of goods x and y represent and on the
optimum solution.

Consider a consumer whose utility function is
u(x, y) = x + y (perfect substitutes)
a. Assume the consumer has income $120 and initially faces the
prices px = $1 and py = $2. How much x and y would they buy?
b. Next, suppose the price of x were to increase to $4. How
much would they buy now?
c. Decompose the total effect of the price change on demand
for x into the substitution effect and the...

Suppose a consumer has the utility function U (x, y) = xy + x +
y. Recall that for this function the marginal utilities are given
by MUx(x,y) = y+1 and MUy(x,y) = x+1.
(a) What is the marginal rate of substitution MRSxy?
(b)If the prices for the goods are px =$2 and py =$4,and if the
income of the consumer is M = $18, then what is the consumer’s
optimal affordable bundle?
(c) What if instead the prices are...

1. A consumer has the utility function U = min(2X, 5Y ). The
budget constraint isPXX+PYY =I.
(a) Given the consumer’s utility function, how does the consumer
view these two goods? In other words, are they perfect substitutes,
perfect complements, or are somewhat substitutable? (2 points)
(b) Solve for the consumer’s demand functions, X∗ and Y ∗. (5
points)
(c) Assume PX = 3, PY = 2, and I = 200. What is the consumer’s
optimal bundle?
(2 points)
2....

A consumer has utility function U(x, y) = x + 4y1/2 .
What is the consumer’s demand function for good x as a function of
prices px and py, and of income m, assuming a
corner solution?
Group of answer choices
a.x = (m – 3px)/px
b.x = m/px – 4px/py
c.x = m/px
d.x = 0

Consider the utility function U ( x,y ) = min { x , 2y }.
(a) Find the optimal consumption choices of x and y when I=50,
px=10, and py=5.
(b) The formula for own-price elasticity of x is
εx,px = (−2px/2px +
py) For these specific values of income, prices, x and
y, what is the own-price elasticity? What does this value tell us
about x?
(c) The formula for cross-price elasticity of x is
εx,py = (py/2px +...

8) Suppose a consumer’s utility function is defined by
u(x,y)=3x+y for every x≥0 and y≥0 and
the consumer’s initial endowment of wealth is w=100. Graphically
depict the income and
substitution effects for this consumer if initially Px=1 =Py and
then the price of commodity x
decreases to Px=1/2.

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...

Suppose a consumer has the utility function u(x, y) = x + y.
a) In a well-labeled diagram, illustrate the indifference curve
which yields a utility level of 1.
(b) If the consumer has income M and faces the prices px and py
for x and y, respectively, derive the demand functions for the two
goods.
(c) What types of preferences are associated with such a utility
function?

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...

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