Question

Consider the utility function U(x,y) = xy Income is I=400, and
prices are initially

px =10 and py =10.

(a) Find the optimal consumption choices of x and y.

(b) The price of x changes, to px =40, while the price of y remains
the same. What are

the new optimal consumption choices for x and y?

(c) What is the substitution effect?

(d) What is the income effect?

Answer #1

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...

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 +...

Given the following utility function and budget
contraints:
U(X,Y) = XY
I = Px (X) + Py(Y)
and given that: Py = 10 , Px=12 and I = 360
Fill in the blanks in the following table (round to two
decimal places):
Part 1: What is the Value of
Qx?
Part 2: What is the Value of
Qy?
Part 3: What is the Optimal
level of utility?

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...

Jane’s utility function has the following form: U(x,y)=x^2
+2xy
The prices of x and y are px and py respectively. Jane’s income
is I.
(a) Find the Marshallian demands for x and y and the indirect
utility function.
(b) Without solving the cost minimization problem, recover the
Hicksian demands for x and y and the expenditure function from the
Marshallian demands and the indirect utility function.
(c) Write down the Slutsky equation determining the effect of a
change in px...

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...

4. Consider an individual making choices over two
goods, x and y with prices px = 3 and py = 4,
and who has income I = $120 and her preferences can be represented
by the utility function U(x; y) =
x2y2. Suppose the
government imposes a sales tax of $1 per unit on good x: ( Hint:
You need to find the initial, final, and hypothetical optimal
consumption bundles, their corresponding maximized utility levels
and/or minimized expenditure and compare. )...

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.

Suppose Rajesh has a utility function resulting in an MRS = Y /
X (from U = √XY) and he has an income of $240 (i.e. M = 240).
Suppose he faces prices PX = 8 and PY = 10. If the price of good Y
goes down to PY = 8, while everything else remains the same, find
Rajesh’s compensating variation (CV).
The answer is CV = -25.34, please show your work

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.

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