Question

Consider a consumer that has preferences given by u(x,y)= x^(2/5) y^(3/5) and a budget of $300. This consumer can purchase either good x or good y. The consumer faces a price of good x of $1 and a price of good Y of $6. What is the income effect of a price decrease of good Y to $1.50? (Note: Round your answer to the nearest whole number. For example, if your answer is 15.75 enter in 16)

Answer #1

Suppose a consumer's preferences are given by U(X,Y) = X*Y.
Therefore the MUX = Y and MUY = X. Suppose
the price of good Y is $1 and the consumer has $80 to spend (M =
80). Sketch the price-consumption curve for the
values
PX = $1
PX = $2
PX = $4
To do this, carefully draw the budget constraints associated with
each of the prices for good X, and indicate the bundle that the
consumer chooses in each...

A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that
MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2)
a. What is the marginal rate of substitution?
b. Suppose that the price of good x is 2, and the price of good
y is 1. The consumer’s income is 20. What is the optimal quantity
of x and y the consumer will choose?
c. Suppose the price of good x decreases to 1. The price of good
y and...

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...

2. Consider a consumer with preferences represented by the
utility function:
u(x,y)=3x+6sqrt(y)
(a) Are these preferences strictly convex?
(b) Derive the marginal rate of substitution.
(c) Suppose instead, the utility
function is:
u(x,y)=x+2sqrt(y)
Are these preferences strictly convex?
Derive the marginal rate of sbustitution.
(d) Are there any similarities or diﬀerences between the two
utility functions?

5. Harry Mazola [4.7] has preferences u = min (2x + y, x + 2y).
Graph the u = 12 indifference curve. Mary Granola has preferences u
= min (8x + y, 3y + 6x). Graph the u = 18 indifference curve.
6. A consumer with m = 60 is paying pY = 2. They must pay pX = 4
for the first 5 units of good x but then pay only pX = 2 for
additional units. The horizontal...

Consider a consumer with a utility function U =
x2/3y1/3, where x and y are the quantities of
each of the two goods consumed. A consumer faces prices for x of $2
and y of $1, and is currently consuming 10 units of good X and 30
units of good Y with all available income. What can we say about
this consumption bundle?
Group of answer choices
a.The consumption bundle is not optimal; the consumer could
increase their utility by...

A consumer has preferences given by U(x, y) = min[x, y].
(a) Calculate the equilibrium quantities of x and y when px = $2,
py = $3
and I = 12.
(b) Suppose px increases to $3 when a per unit tax of $1 is placed
on x.
What is the new value of x and how much tax revenue is
raised?
(c) Suppose that the same tax revenue is raised by an income tax
as
opposed to a per...

Consider a consumer with preferences represented by the utility
function
u(x,y)=3x+6 sqrt(y)
(a) Are these preferences strictly convex?
(b) Derive the marginal rate of substitution.
(c) Suppose instead, the utility function is:
u(x,y)=x+2 sqrt(y)
Are these preferences strictly convex? Derive the marginal rate
of substitution.
(d) Are there any similarities or differences between the two
utility functions?

Consider a consumer with preferences represented by the utility
function:
U(x,y) = 3x + 6 √ y
Are these preferences strictly convex?
Derive the marginal rate of substitution
Suppose, the utility function is:
U(x,y) = -x +2 √
y
Are there any similarities or differences between the two
utility functions?

Consider a consumer with Cobb-Douglas preferences over two
goods, x and y described by the utility function u(x, y) = 1/3ln(x)
+ 2/3n(y) 1. Assume the prices of the two goods are initially both
$10, and her income is $1000. Obtain the consumer’s demands for x
and y.
2. If the price of good x increases to $20, what is the impact
on her demand for good x?
3. Decompose this change into the substitution effect, and the
income effect....

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