APPLIED ECON 440.601 — Midterm Exam
DUE: Wednesday, March 16th, 2022, 8 am EST
The solutions to this exam should be submitted via the link under “Assignment Guidelines” by 8 am EST, Wednesday, March 16th, 2022. No late exams will be accepted, no exceptions. This exam is open book, open note. However, please do not communicate with others about the exam during the relevant period.
Note: Interpretations ofthe outcomes are required for full credit.
Problem 1 (40 Points)
Inhabitants from a country named Nenseland have two types of utilities.
ua (xa, ya) = xa(2)/3 . ya(1)/3
ub (xb, yb) = xb(1)/3 . yb(2)/3
Where x is the consumption of luxury goods and y is the consumption of non-luxury goods for individuals with utility types a and b. Considering this information, please answer the following questions.
a) If you are an individual of this country, what type do you think you are? Explain your answer (5 points).
b) Find the Marshallian demand for both goods considering both types of individuals (start from scratch) and interpret (10 points).
c) Calculate the substitution effect and the income effect for both types of individuals and interpret (15 points).
d) Nenseland decided to introduce a tax on luxury goods, so discuss the implications of this policy in the light of the lump sum principle (10 points).
Problem 2 (15 Points)
Consider the following production function: Q = Kα Lβ
a) Derive the cost function (8 points).
b) Draw the AC and MC when α + β > 1 (7 points).
Problem 3 (15 Points)
Maximize XYZ s.t. 2X+30Y+150Z = 900. If X is the quantity of bus rides, Y is the quantity of train rides, Z the quantity of flight tickets, and 900 is the total income for transport, interpret your final answer based on this information. How can you be certain that your final answer is a maximum point?
Problem 4 (30 Points)
Tricolor is a company of selling jerseys and is deciding where to locate its production plant. If it locates in region A, the production function is described by the formula below:
fA (k, l) = [k2 + l2]3/2
If it locates in region B, then the production function is the following:
fB (k, l) = k1/2l1/2
a) Considering that the firm wants to be located where it can have the maximum returns to scale, where should it be located? Explain your answer (10 points).
b) Considering the prices of labor and capital as w and v, respectively, and output price asp (firm is price taker), find the optimal quantity of labor in the short-run in region B when capital is fixed at level k1. At the optimal level, what happens if price of labor increases? Interpret your answer (10 points).
c) Imagine that a technological change occurred in region B and its production function is now given by
fB (k, l) = 2kl
Does it change where Tricolor would have its plant based on returns to scale? Explain your answer (10 points).