Problem Set 3
Microeconomics 1
Aljoscha Janssen*
Hand-in solutions by noon the 2nd of February. Individual answers are required. You hand them in on the
fifth floor of the SOE in my postbox (right of the elevator) or in class. Do not forget to indicate your name,
and student number clearly!
Problem 1.1. Zijia worked as a scuba diver teacher in Bintan last winter and spent all of her income each
week (1200 units of the local currency som) on beer and candy (all other expenses were paid by her employer).
Assume that the price of beer was 60 som per liter and the price of candy 60 som per hg. Draw Zijia’s budget
constraint.
Problem 1.2. If she buys 10 liters of beer, how much candy can she afford?
Problem 1.3. Assume that her utility function is given by U =
√
beer × candy. Draw the indifference curve
that corresponds to a utility level of 10 in the same diagram as 1.1.
Problem 1.3. If she instead were to buy 15 liters of beer, how much candy can she afford? What would her
utility level be then?
Problem 1.4. Assume that the price of candy rises to 80 som. Show the new budget constraint.
* ajanssen@smu.edu.sg
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Problem 2.1. In Dubois, Griffith and Nevo (2014), “Do Prices and Attributes Explain International Differences in Food Purchases?, American Economic Review they examine consumption patterns for food for
French, UK and US consumers. In their Table 2 they summarize some differences in consumption patterns
– how many calories, how much proteins etc do people on average consume per day and what is the cost.
Briefly discuss possible reasons for differences in consumption patterns between France and US.
Problem 2.2. Assume that relative prices for different types of food differ between these countries (which they
do). For simplicity assume that in each country there are only two goods – confit de canard and pizza - and that
they are imperfect substitutes. Confit is relatively cheap in France compared to in the US. Show how a French
household meeting US prices (instead of French prices) would consume using a figure with an indifference curve
and US and French relative prices.
Problem 3.1. Albert loves fitness. He consumes only protein shakes (x) and protein bars (y). His utility
function is u(x, y) = xy + 10y. Draw the indifference curve of Albert.
Problem 3.2. Albert does not like to work. His income is 90 $ per week as his mum supports his lifestyle.
If a protein shake (x) as well as the protein bar (Y ) cost 1 $ how will the budget constraint look? Draw the
budget constraint in the diagram of 2.1.
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Problem 3.3. Solve Albert’s choice problem graphically a well as analytically. How many shakes and bars
will he consume in optimum?
Problem 4.1. Wei eats durian (x) and apples (y). His utility function is u(x, y) = xa y b . Further, he has an
income of I. What is the optimal fraction of income spent on durian?
Problem 4.2. What is the optimal amount if cash spent on apples?
Problem 4.3. What is the optimal quantity of durian?
Problem 4.4. Consider the following parameters: a = 4, b = 8, px = 5, py = 10, I = 60. Find the slope of the
indifference curve at the optimal bundle.
Problem 5.1. Solve the following consumer choice problem:
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max
u(x, y) = min{x, 2y} 2
x,y
s.t.
2x + 3y = 30
Problem 6. Use the Lagrange Multiplier Method to solve the following maximization problem:
max
x,y
u(x, y) = 4x2 + 3xy + 6y 2
s.t. x + y = 56
Problem 7. Solve the following choice problem
max
x,y
u(x, y) = x2 + y 2
s.t. x + y = 5
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