UNIVERSITY OF
WATERLOO
Department of Economics
ECON 393
Midterm 1
L-A. Busch
Instructions:
October 4, 2023
This is a closed book exam. No aids are allowed or required. Length 70 minutes.
Please write your name and student number on the exam booklet, and return the completed exam booklet when asked. You may keep the question sheet. Please write legibly and
ideally with a high contrast (i.e. consider not using a pencil but a pen ... )
Part marks are awarded for method. As a matter of fact the method is often more
important than the answer. Show/demonstrate how you arrived at the answer you provide.
PART 1: DEFINITIONS
1. (4 marks) Define an ’Engel Curve’
2. (4 marks) Define ’luxury good’
3. (4 marks) Define EITHER the Price-Offer Curve OR the Income Expansion Path
4. (4 marks) Define the Compensating Variation according to Slutsky (’Slutsky Compensation’).
PART 2: BUDGETS
1. (8 marks) Consider a worker who generates income via selling his leisure time as
’labour’. Suppose there also is one consumption good. For simplicity we will take
the price of the consumption good as 1, and denote the price of labour/leisure time
(per hour) as w. Both consumption and labour/leisure are assumed to be infinitely
divisible (so we are in R2+ as usual.) This worker has an endowment of consumption
good of 10 units. The worker has an endowment of 10 hours of labour/leisure time
to sell. Obviously time cannot be bought! We can think of this situation either in a
leisure - consumption space (i.e. leisure on the horizontal axis and consumption on the
vertical) or in terms of labour - consumption space (so now labour is on the horizontal
and consumption on the vertical). It does not matter. Pick one of these viewpoints
and carefully define the budget set of the worker. A diagram is useful, but appropriate
mathematical expression(s) are also needed.
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2. (8 marks) Consider a 2 period model with two consumption goods in each period.
We will use the notation xt to denote the level of good x consumption in period t.
Similarly y t denotes good y consumption in period t. The goods have prices that may
differ across good and time. So we have four prices: p1x , p2x , p1y , p2y .
The consumer has income of m1 in period 1 and m2 in period 2. Everything is nice
and divisible, and all these variables are non-negative.
We now introduce a ’Savings Contract’: this is a contract that in return for one unit
of money/income in period 1 will pay out (1 + r) units of money/income in period 2.
Denote the number of those contracts (infinitely divisible again) by S. The consumer
can ’buy’ such a contract (i.e. actually save: S > 0) or ’sell’ it ( S < 0 in which case
she receives the income in period 1 and has to repay in period 2, i.e. borrows).
Write down the consumer’s budget constraint(s).
PART 3: PROBLEMS
1. (8 marks) Consider a consumer with preferences represented by u(x1 , x2 ) = min{2x1 , x2 }.
What are the quantities demanded at income 20 and prices (2, 1)? (SHOW your
work!)
Suppose the price of good 1 falls from 2 to 3/2. What is the quantity demanded
now?
What is the Slutsky Compensation for this price change?
2. (8 marks) We tend to predominantly look at two good problems. Because the pictures
are pretty (and can be drawn) one supposes. But it sometime has strong implications
on the results that are possible. Here are two examples. I want you to argue/explain
why these results are true (i.e. ’prove’ them by a rigerous logical argument in words
with a diagram or using mathematical symbols. Hint: either way, Walras’ Law (all
income must be spent) is at the crux of the argument.)
With just two goods both goods cannot be inferior goods.
Fact: with just two goods both can be normal goods. Prove/argue that both of
them cannot be necessary goods.
Closing Thought: (4 marks)
Why o why would one want to use ’netput vectors’ in modelling the production side?
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