Question

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) = (16, 9). Find the minimized cost C(400). What is the cost-minimizing input bundle (x ∗ , y∗ )?

(D) Give a complete geometric illustration of this firm’s cost minimization. On a single diagram, draw the firm’s level-400 isoquant, the isocost lines, and the cost-minimizing input bundle

Answer #1

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,...

Problem 1. Consider the Cobb-Douglas production function f(x, y)
= 12x 0.4y 0.8 .
(A) Find the intensities (λ and 1 − λ) of the two factors of
production. Does this firm have decreasing, increasing, or constant
returns to scale? What percentage of the firm’s total production
costs will be spent on good x?
(B) Suppose the firm decides to increase its input bundle (x, y)
by 10%. That is, it inputs 10% more units of good x and 10%...

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...

Problem 5. Suppose that a firm’s production function is f(x, y)
= 20x 0.7y 0.3 . Starting from the input bundle (x, y) = (40, 60),
how much extra output will the firm get if it increases x from 40
to 41? How many units of output will the firm lose if x decreases
from 40 to 39

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...

1. Consider the general form of the utility for goods that are
perfect complements.
a) Why won’t our equations for finding an interior solution to the
consumer’s problem work for this kind of utility? Draw(but do not
submit) a picture and explain why (4, 16) is the utility maximizing
point if the utility is U(x, y) = min(2x, y/2), the income is $52,
the price of x is $5 and the price of y is $2. From this picture
and...

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 = _____.

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:
(a) Calculate the substitution effect and Income effect (on good
x) after the price change. Also Illustrate on a graph.
(b) Find the government tax revenues...

1. A. The Cobb-Douglas production function, f(x,y)=40x^1/4y^3/4,
describes the production of a company for which each unit of labor
costs $100 and each unit of capital costs $125. For a new project,
the company has allocated $60,000 for labor and capital. Find the
amount of money that the company should allocate to labor and
capital to maximize production.
B. The marketing department of a business has determined that
the demand for a product can be modeled by p=(50/(square root of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 35 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago