Utility & Choice
Problems
Guy Numa, PhD
ECON 306-FTU Intermediate Microeconomics December 2024
Problem 1
Use supply and demand curves to illustrate the impact of the following
events on the market for coffee:
a. The price of tea goes up by 150 %.
b. A study shows that the consumption of caffeine raises the incidence
of cancer.
c. A frost kills half of the coffee bean crop.
d. The price of styrofoam coffee cups goes up by 250 %.
a. An increase in the price of a substitute, such as tea, will increase
demand for coffee, raising the equilibrium price and quantity.
b. The study will reduce demand for caffeine drinks as
individuals drink less to reduce the risk of cancer, lowering the
market equilibrium price and quantity.
c. The frost will reduce supply, raising the equilibrium price while
lowering the equilibrium quantity.
d. Increasing the price of an input for coffee cup will reduce
supply, increasing market price and reducing market quantity.
Problem 2
The demand for honey is by Qd = 600 − 2P while the supply is Qs =
300 + 4P.
a. Sketch the supply and demand curves on a diagram and show
where the equilibrium occurs.
b. Determine the market equilibrium price and quantity of honey.
Problem 2
Problem 2
b)
600 − 2𝑃 = 300 + 4𝑃
300 = 6𝑃
50 = 𝑃
Plugging P = 50 back into either the demand or supply equation yields
Q = 500.
Problem 3
Consider the following sequence of changes in the demand and supply for cab service
in Hanoi. P is the price per mile, while Q is the total length of cab rides over a month (in
thousands of miles).
• January: Initial demand and supply are given by the equations Qs = 30P - 30 (when P
≥ 1), and Qd = 120 - 20P
• February: Due to higher prices of gasoline, the supply of cab service changed to
Qs = 30P - 60 (when P ≥ 2).
• March: Over the spring break, the demand for taxi service was higher and therefore
demand curve was given by the equation Qd = 140 - 20P.
a. For each month, find the equilibrium price and quantity.
b. Draw a diagram illustrating the equilibrium prices and quantities.
Problem 3
We find equilibrium price by solving Qs = Qd, which is 30P – 30 = 120 – 20P. When we
have equilibrium price (P = 3), we can substitute it to either the demand function or
supply function and obtain equilibrium quantity equal to Q = 60. Therefore, the
equilibrium price in January is equal to P = 3 and equilibrium quantity is equal to Q = 60.
In February: Qs = Qd yields 30P – 60 = 120 – 20P
New equilibrium price per mile is equal to P = 3.6, while the quantity demanded is Q = 48
=> supply falls.
When demand goes up in March: Qs = Qd yields 30P – 60 = 140 – 20P
Equilibrium quantity is the same as in January (Q = 60), but price is higher and equal to
P = 4.
Problem 3
Problem 4
Consider the utility function U(x, y) = 𝑦 𝑥
a) Calculate the marginal utilities of x and y.
b)Does the consumer believe that more is better for each good?
c) Do the consumer’s preferences exhibit a diminishing marginal
utility of x? Is the marginal utility of y diminishing?
Problem 4
a. MUx =
!
" #
and MUy = 𝑥
b. Since U increases whenever x or y increases, more of each good is
better. This is also confirmed by noting that MUx and MUy are both
positive for any positive values of x and y.
c. Given that MUx =
!
" #
, as x increases (holding y constant), MUx falls..
However, MUy = 𝑥. As y increases, MUy does not change.
Therefore, MUy is constant, not diminishing.
Problem 5
For the following sets of goods, draw two indifference curves, U1 and U2, with
U2 > U1. Draw each graph placing the amount of the first good on the horizontal
axis.
a) Hot dogs and tacos (the consumer likes both and has a diminishing marginal
rate of substitution of hot dogs for tacos)
b) Sugar and honey (the consumer likes both and will accept an ounce of
honey or an ounce of sugar with equal satisfaction)
c) Peanut butter and strawberry jam (the consumer likes exactly 2 ounces of
peanut butter for every ounce of strawberry jam)
d) Cashew nuts (which the consumer neither likes nor dislikes) and ice cream
(which the consumer likes)
Problem 5
Problem 5
Problem 6
Malia consumes apples and oranges (the only fruits she eats). She has decided
that her monthly budget for fruit will be $50. Suppose that one apple costs
$0.25, while one orange costs $0.50. Let x denote the quantity of apples and y
denote the quantity of oranges that Malia purchases.
a. What is the expression for Malia’s budget constraint?
b. Draw a graph of Malia’s budget line.
c. Show graphically how Malia’s budget line changes if the price of apples
increases to $0.50.
d. Show graphically how Malia’s budget line changes if the price of oranges
decreases to $0.25.
Problem 6
a. 0.25x + 0.50y ≤ 50
b.
Problem 6
c.
Problem 6
d.