Assignment Questions
Suppose that Sally’s preferences over baskets containing milk (good x), and coffee (good
y ), are described by the utility function U(x, y ) = xy + 2x. Sally’s corresponding marginal
utilities are,
MUx = y + 2 and MUy = x.
Use Px to represent the price of milk, Py to represent the price of coffee, and I to represent
Sally’s income.
Question 1: Suppose that the price of milk is Px = $1 per litre, the price of coffee is
Py = $4 per cup, and Sally’s income is I = $40. Without deriving the optimal consumption
basket, show that the basket with x = 16 litres of milk, and y = 6 cups of coffee, is NOT
optimal. (2 Marks)
Question 2: Derive the expression for Sally’s marginal rate of substitution. (1 Mark)
Question 3: Derive Sally’s demand for coffee as a function of the variables Px , Py and
I. (i.e. Do NOT use the numerical values for Px , Py and I, from question 1.) For the
purposes of this question you should assume an interior optimum. (3 Marks)
Question 4: Derive Sally’s demand for milk as a function of the variables Px , Py and I. (i.e.
Do NOT use the numerical values for Px , Py and I, from question 1.) For the purposes
of this question you should assume an interior optimum. (1 Mark)
Question 5: Describe the relationship between Sally’s demand for milk and,
(a) Sally’s income;
(b) the price of milk;
(c) the price of coffee.
Your answers must reference the demand function that you derived in question 4, AND
use the correct term to describe the relationship. (6 Marks)
Question 6: Suppose that Px = $1 and I = $40. Find the equivalent variation for an
increase in the price of coffee from Py1 = $4 to Py2 = $5. (7 Marks)

Price Theory

Assignment 2 { Market Power

Firms 1 and 2 produce horizontally dierentiated products. The demand for rm 1’s
product is given by the equation,
Q1 = 100 ?? P1 +
P2
2
:
The demand for rm 2’s product is given by the equation,
Q2 = 200 ?? 4P2 + 2P1:
Firm 1’s marginal cost is MC1 = $10, while rm 2’s marginal cost is MC2 = $20. The
two rms compete in Bertrand competition, by simultaneously selecting prices.
Question 1: What is the equation of rm 1’s reaction function? (3 Marks)
Question 2: What is the equation of rm 2’s reaction function? (3 Marks)
Question 3: Find the equilibrium prices. (2 Marks)
Question 4: Find the equilibrium prots. (2 Marks)
Question 5: Which rm enjoys the greater market power? Brie
y explain your answer.
(2 Marks)
Now suppose that rm 2 adopts a new technology that lowers it’s marginal cost to
MC2 = 5. (Assume that demand for each rm’s product, and rm 1’s marginal cost
are unchanged.)
Question 6: Find the new equilibrium prices, quantities and prots. (4 Marks)
Question 7: What has happened to rm 1’s Lerner Index of market power? Brie
y
explain why it has changed. (4 Marks)
1

Price Theory

Assignment 2 { Market Power

Firms 1 and 2 produce horizontally dierentiated products. The demand for rm 1’s
product is given by the equation,
Q1 = 100 ?? P1 +
P2
2
:
The demand for rm 2’s product is given by the equation,
Q2 = 200 ?? 4P2 + 2P1:
Firm 1’s marginal cost is MC1 = $10, while rm 2’s marginal cost is MC2 = $20. The
two rms compete in Bertrand competition, by simultaneously selecting prices.
Question 1: What is the equation of rm 1’s reaction function? (3 Marks)
Question 2: What is the equation of rm 2’s reaction function? (3 Marks)
Question 3: Find the equilibrium prices. (2 Marks)
Question 4: Find the equilibrium prots. (2 Marks)
Question 5: Which rm enjoys the greater market power? Brie
y explain your answer.
(2 Marks)
Now suppose that rm 2 adopts a new technology that lowers it’s marginal cost to
MC2 = 5. (Assume that demand for each rm’s product, and rm 1’s marginal cost
are unchanged.)
Question 6: Find the new equilibrium prices, quantities and prots. (4 Marks)
Question 7: What has happened to rm 1’s Lerner Index of market power? Brie
y
explain why it has changed. (4 Marks)
1