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Midterm

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Economics

ECO206Y1

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Fall

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ECO206 – Microeconomic Theory
1. Midterm I Structure
Based on analysis of past midterms, there are five main topics that are covered in the first midterm of
ECO206: Budget constraints, utility maximization, income and substitution effects, government
grants/taxes and labor supply. The midterm is usually about 2 hours long and consists of 3 to 5
questions with 3 to 5 sub-questions per question. The total number of questions, including sub-
questions, is roughly 12 to 15.
2. Midterm I Statistics
Topics/Years 2009 2011* 2012
Budget Constraints 1 1 1
Utility Maximization 2 4 7
Income and 1 1 1
Substitution Effects
Government 4 5 2
Grants/Taxes
Labor Supply 4 3 4
Total 12 14 15
*In Midterm I of 2011, the test also included two questions on topics: normal goods and cross-price elasticity of demand. Neither
of these topics appeared in midterm I of 2009, 2012.
Midterm I Questions Statistics
8
7
6
Budget Constraints
5
Utility Maximization
4 Income and Substitution Effects
3 Government Grants/Taxes
2 Labor Supply
1
0
2009 2011 2012 Topic 1: Budget Constraints
Knowledge Summary:
The budget constraint, for the purpose of the first midterm, gives a combination of 2 goods (x
and y) that the individual can consume given his/her constraints: price of good x (p ), xrice of
good y (p y and the individual’s income (E).
Critical assumption: the individual spends all his income on consuming goods x and y. Therefore
we can write the budget constraint as: p xx + p *y = I
Furthermore, the budget constraint is a linear function and this tells us that the consumer is a
price taker.
The three properties above help us derive the budget constraint graphically:
Slope: - (px)/(py), the slope is the
measure of the opportunity cost
Moving from left to right along the
budget constraint implies that we are
consuming more of x and less of y.
A change in income (I) causes a
shift in the budget constraint
A change in p cxuses the budget
constraint to pivot through the vertical
intercept (0, I/y ). An increase in x causes
the budget constraint to pivot inward. A
decrease in pxcauses the budget constraint
to pivot outward.
A change in p cyuses the budget
constraint to pivot through the horizontal intercept (I/px,0). Movement of the budget constraint is
identical to the movement described in the previous bullet point.
Summary of Questions to be asked:
Graphical representation of a budget constraint given 2 goods, their respective prices and the
consumer’s income: graph the intercepts as shown in the graph above and connect them with
a line, label the intercepts, the value of the slope and the axes.
Graphical change in the budget constraint due to changes in prices and/or income: recall –
change in income shift, and change in price change in slope/pivot
Derive the budget constraint equation in order to solve an optimization problem: refer to
utility maximization section below to see an optimization problem. Related Past Test Questions:
2012 Midterm 1 Question 1
2009 Midterm 1 Question 4a-i Topic 2: Utility Maximization
Knowledge Summary:
Key Components and Formulas:
Utility Function: mathematical representation of a preference order, assigning a number to each
commodity bundle (x,y). Denote this function as U(x,y). The utility function helps us deduce
which commodity bundles the consumer best prefers and least prefers.
Indifference Set: set of bundles that satisfies U(x)=Ȗ, for some arbitrary utility level Ȗ (i.e. Ȗ is
a constant). These bundles are represented by an indifference curve shown below. All bundles on
this indifference curve are equally preferred; therefore consumers are indifferent to any of them.
Indifference curves to the right have higher utility and to the left have lower utility.
Marginal Rate of Substitution (MRS): is the slope of the indifference curve. It shows how
much of good y a consumer is willing to give up, to consume more of x holding utility constant at
Ȗ. The formula of the MRS is:
=
How to derive the MRS:
Totally differentiate the utility function U(x,y)=Ȗ
Rearranging gives us:
This represents the negative slope of the indifference curve. The MRS gives us the consumer’s
willingness to substitute one good for another. With good y on the vertical axis and good x on the
horizontal axis, the MRS represents the additional utility a consumer receives from consuming
one more unit of good x (good on horizontal axis) and the loss of satisfaction from consuming
less of good y (good on vertical axis). Utility Maximization Problem: involves solving a constrained optimization problem combining
a (i) utility function and a (ii) budget constraint. The utility function U(x,y) is the objective
function and it is maximized subject to the budget constraint we derived earlier: p *x + p *y = I
px*x + p yy = I
To solve a maximization problem, it is essential to use the optimality condition:
Solving for x and y using this optimality condition and then substituting them into the budget
constraint gives the optimal consumption bundle (x*, y*), example provided in past midterm
questions below.
Graphically, it is the point of tangency between the indifference curve and the budget constraint.
2 Methods to solve: (i) substitution or (ii) Lagrangean
Summary of Questions to be asked:
Derive the budget constraint, the marginal utilities of each good and the MRS
State the optimality condition
Solve a traditional constrained optimization problem involving maximizing a utility function
subject to a budget constraint; may or may not specify method desired.
Graphically represent the point of tangency between the indifference curve and the budget
constraint
Related Past Test Questions:
2012 Midterm I Question 3 2009 Midterm I Question 1
Topic 3: Income and Substitution Effects
Knowledge Summary:
The total effect of a price change can be decomposed into two effects: 1) the substitution effect
and 2) the income effect
We use substitution and income effects in order to identify and classify different types of goods:
normal goods, inferior goods, and Giffen goods.
Substitution effect is usually consistent for all types of goods, except Giffen goods: if the price of
good x decreases and the price of good y remains constant, we will substitute more of good y for
good x (i.e. if price of x decreases, quantity demanded of x increases and vice versa). Substitution
effect induces an income effect because we have more income left over due to the decrease in
price.
Income effects differ based on the type of good in question:
- Normal good: if income increases, quantity demanded

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