Chapters 5 & 6 Homework #3 Due: September 26th, 2017
ECON 361 – Intermediate Microeconomics Page 1 of 1
1. Thomas has a quasi-linear utility function of the form
U (x; y) = x3 + 2y:
a) What are Thomas’s marginal utility functions, MUx
b) Suppose I = 30, Px = 12, and Py = 2. What is utility
c) Derive Thomas’s demand curve for x (in terms of ex-
ogenous variables I, Px and Py).
d) Derive Thomas’s demand curve for y (in terms of ex-
ogenous variables I, Px and Py).
2. Frank’s preferences over oranges (x) and other goods (y)
are given by U (x; y) =
xy, and he has an income of
I = $120. (Hint: Might need calculator)
a) What are his marginal utility functionsMUx &MUy?
b) Calculate the optimal basket when Px = 6 & Py = 3.
c) Suppose Px decreases to Px = 1, nd the new optimal
d) Calculate the income and substitution eects when Px
decreases to Px = 1.
e) What is the compensating variation of the price
f) What is the equivalent variation of the price change.
3. Suppose the market for cars has two segments, businesses
and home users. The demand curve for cars by businesses
is P = 120 40Qb, where Qb is the quantity of cars
demanded by businesses with the price is P. The demand
curve for cars by home users is P = 40 10Qh, where
Qh is the quantity of cars demanded by home users when
the price is P. Both businesses and home users will never
demand negative amounts of cars, so for suciently high
prices, the demand will be 0.
a) Graph the demand curves for each segment, and draw
the market demand curve for cars.
b) Write the equation for the demand curve for all prices
P 0 (make sure that it matches with part (a)).
c) When the price is P = $20, what is the consumer
surplus for businesses, home users, and the market as
4. A rm uses the inputs of fertilizer, labor, and hothouses
to produce roses. Suppose that when the quantity of
labor and hothouses is xed, the relationship between the
quantity of fertilizer and the number of roses produced
is given by the following table:
Tons Fertalizer 0 1 2 3 4 5 6 7 8
1000’s of Roses 0 0:5 1 1:7 2:2 2:5 2:6 2:5 2
a) What is the average product of fertilizer when 4 tons
b) What is the marginal product of the sixth ton of fer-
c) Does this total product function exhibit diminishing
marginal returns? If so, over what quantities of fer-
tilizer do they occur?
d) Does this total product function exhibit diminishing
total returns? If so, over what quantities of fertilizer
do they occur?
5. A rm is required to produce 50 units of output using
quantities of labor and capital (L;K) = (3; 8). For each
of the following production functions, state whether it is
possible to produce the required output with the given
input combination. If it is possible, state whether pro-
ducing Q = 50 with input combination is technically ef-
cient or inecient.
a) Q = 8L + 4K
b) Q = 10
c) Q = min f17L; 7Kg
d) Q = 2KL + L 6.
6. Consider the production function Q = KL2 L3.
a) Sketch a graph of at least 4 isoquants from this pro-
b) Does this production function have an uneconomic
region? If so, describe the region algebraically (Hint:
your answer will be an inequality like this: K < L)?
7. A rm’s production function is Q = 3L1=3K2=3.
a) Does this production function have constant, increas-
ing, or decreasing returns to scale?
b) Determine MRTSL;K for this production function.
c) What is the elasticity of substitution for this produc-
tion function? (Hint: what type of production func-
tion is this?)
8. A rm’s production function is initially Q1 = K
Over time, the production function changes to Q2 =
a) Does this change represent technological progress?
b) Is this change labor saving, capital saving, or neutral?