Question

Dan’s preferences are such that left shoes (good x) and right shoes (good y) are perfect complements. Specifically, his preferences are represented by the utility function U (x, y) = minimum{x, y}.

(a) Draw several of Dan’s indifference curves. Which bundles are at the “kink- points” of these curves?

(b) Assume that Dan’s budget for shoes is M = 10 and that the
price of a right shoe is py = 2. Find and draw Dan’s demand curve
for left shoes (quantity demanded as a function of the price
px).

Hint: Given the shape of indifference curves from part (a) we can’t
use tangency to find the optimal affordable bundle, use instead the
shape of the curves to determine its location.

(c) If the price of right shoes decreases to py = 1 (income is still M = 10), what is the new demand curve for left shoes? Compare the new demand curve to the previous one and determine whether x and y are complements or substitutes.

Answer #1

Suppose it is possible to buy left shoes for a price of $35/shoe
and right shoes for a price of $45/shoe. Alex has an annual budget
of $1600 for buying shoes, and she has, like most people two
feet.
Draw Alex’s budget line between left shoes (on the horizontal
axis) and right shoes (on the vertical axis). Draw a few of her
indifference curves, and show her optimal choice. How many left
shoes and how many right shoes does she...

Question 6 The demand for good x is given by x ∗ = 60 − 4Px + 2M
+ Py, where Px is the price of good x, Py is the price of good y,
and M is income. Find the own-price elasticity of demand for good x
when Px = 20, Py = 20, and M = 100. Is x an ordinary or giffen
good? Explain.
Question 7 The demand for good x is given by x ∗ =...

Suppose the demand curve for good X is of the form:
qx=1000 + I – 50px -20py. Suppose,
px=$10, py=$10, and income (I)=$100.
1)
Cross price elasticity of demand between X and Y = -1/2, and X
and Y are complements.
2)
Cross price elasticity of demand between X and Y = 1/2, and X
and Y are complements.
3)
Cross price elasticity of demand between X and Y = -1/2, and X
and Y are substitutes.
4)
Cross price...

Suppose that the demand function for good x is given by
x = 10 - 2px + py + 0.5M, where
M=10 is income and px = 2 and py =
5.
(a) Calculate the own price elasticity of demand.
(b) Calculate the cross price elasticity of demand. Are the
goods substitutes or complements?
(c) Is the good normal or inferior? Calculate the income
elasticity of demand.
(d) Is the good a necessity or a luxury?

Consider the Leontiev (perfect complements) production function
f(x, y) = M in x 9.6 , y 5.2 .
(A) How many units of good y would be a perfect complement for 1
unit of good x? What is the equation of the firm’s kink line?
(B) Assume the firm has a production quota of q = 400 units.
Graph the firm’s level-400 isoquant. What are the coordinates of
the kink?
(C) Suppose the input prices are (px, py) = (16,...

Indifference curves for goods x and y can be right angles
under
A. Perfect substitutes
B. Perfect complements
C. diminishing marginal rate of substitution
D. rising opportunity costs

A wealthy consumer's preferences are strictly convex and his
demand for good X (disinfectant wipes) is independent of his income
and given by
X = 60.9 - 3.7 Px/Py
where Px and Py are respectively the price
of good X and the price of good Y.
Suppose prices are such that the consumer buys 5 units of good X
in order to maximize his utility. What is the consumer's marginal
rate of substitution (of good X in terms of good...

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.

Problem 3. Consider the Leontiev (perfect complements)
production function f(x, y) = M in x 9.6 , y 5.2 .
(A) How many units of good y would be a perfect complement for 1
unit of good x? What is the equation of the firm’s kink line?
(B) Assume the firm has a production quota of q = 400 units.
Graph the firm’s level-400 isoquant. What are the coordinates of
the kink?
(C) Suppose the input prices are (px, py)...

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...

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