Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
EC 2220: Lecture 4 Static Model Consumers and Firms
Baxter Robinson
University of Western Ontario
September 2023
1
Micro-Founded Models
Firm Decisions
Topics
Consumer Decisions
1
Introduction to Macroeconomics
Williamson Text
Chapters 1,2,3
2
3
Economic Growth
Agriculture (Malthus) and Capital (Solow)
Convergence and Human Capital
Chapter 7
Chapter 8
4
5
Static Model
Consumers and Firms
Governments and Labour Market Equilibrium
Chapter 4
Chapter 5
6
7
Dynamic Model
Consumption-Savings
Imperfect Credit Markets
Chapter 9
Chapter 10
8
Investment and General Equilibrium
Chapter 11
Midterm
2
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Lecture 4: Static Model Consumers and Firms
• Micro-Founded Models
• Firm Decisions:
▶ Hire Labour
▶ Graphical Approach
▶ Mathematical Approach
• Consumer Decisions:
▶
▶
▶
▶
▶
Indifference curves
Budget constraints
Graphical Approach
Mathematical Approach
Exercises
3
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
What We Have Done So Far
• Lectures 2 and 3: Three Simple Models of Economic Growth
▶ Malthusian Model
▶ Solow Model
▶ Human Capital Model
• Assignment: Comparing theories of economic growth to data
• These models were limited in many ways
▶ People behaved a certain way by assumption
4
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Models without Decisions
• In all the models so far, we have assumed how people behaved
▶ Malthusian: Assumed how population grows
▶ Solow: Assumed how much people saved
▶ Human Capital: Assumed how much people invested in education
• What if we could model these decisions?
▶ Malthusian: Have people decide how the population grows
▶ Solow: Decide how much to save and how much to spend
▶ Human Capital: Decide how much to invest in education
5
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Models with Decisions
• In the real world people make these decisions based on incentives
▶ Need models of these incentives and decisions
• Micro-Founded Models
▶ Individual agents will make individual decisions
▶ Microeconomics studies these decisions and can help inform
▶ Study how these decisions will change macroeconomic aggregates
6
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
A Micro-Founded Theory of Decision Making
• Agents have some goal they are trying to maximize
▶ Firms try to maximize profits
▶ People try to maximize their utility
• They may be subject to some constraints:
▶ Firms can only produce so much output given their inputs
▶ People can only afford so many goods
• We can embed these preferences and constraints in an optimization problem
7
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Why Are Micro-Founded Models Useful?
• Is this a perfect description of how people actually behave?
▶ No! People are much more complicated
▶ Not possible to perfectly predict
• Is this more useful than just assuming how they react?
▶ Yes!
▶ We can think about how people will respond to changes in:
• Government policy
• Economic shock
8
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Micro-Founded Models in this Course
• Static Model: One time period
▶ Lecture 4 and 5
▶ Workers and Firms
▶ Labour Market Equilibrium
• Dynamic Model: Multiple time periods
▶ Consumers saving
▶ Lecture 6, and 7
• Investment Model
▶ Firm investing
▶ General Equilibrium
▶ Lecture 8
9
Micro-Founded Models
Firm Decisions
Topics
Consumer Decisions
1
Introduction to Macroeconomics
Williamson Text
Chapters 1,2,3
2
3
Economic Growth
Agriculture (Malthus) and Capital (Solow)
Convergence and Human Capital
Chapter 7
Chapter 8
4
5
Static Model
Consumers and Firms
Governments and Labour Market Equilibrium
Chapter 4
Chapter 5
6
7
Dynamic Model
Consumption-Savings
Imperfect Credit Markets
Chapter 9
Chapter 10
8
Investment and General Equilibrium
Chapter 11
Midterm
10
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Lecture 4: Static Model Consumers and Firms
• Micro-Founded Models
• Firm Decisions:
▶ Hire Labour
▶ Graphical Approach
▶ Mathematical Approach
• Consumer Decisions:
▶
▶
▶
▶
▶
Indifference curves
Budget constraints
Graphical Approach
Mathematical Approach
Exercises
11
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Firm Decisions Intuition
• Firms are going to choose how many workers to hire
▶ More workers means more output
▶ More workers means higher wage bills
• Firms are going to have a fixed stock of capital
▶ Later: Firms will choose the level of capital stock
• Firms choose how much labour to hire in order to maximize profits
12
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Firm Decisions
• Production function
Y = zF (K , N)
▶ Y is the firm’s output
▶ z is total factor productivity
▶ K is capital
▶ N is labour
• MPK =
∂Y
∂K
is the marginal product of capital
• MPN =
∂Y
∂N
is the marginal product of labour
13
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Properties of the Production Function: Monotone
Production Function, Fixing the Quantity
Production
Function, Fixing the Quantity
More inputs produces more output
of of
Capital and Varying the Quantity of
of Labor
and>Varying
the Quantity
• MP
0
K
Labour Capital • MP > 0
N
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
5-31
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
145-30
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Properties of the Production Function: Decreasing Marginal Products
Production Function, Fixing the Quantity
Production
Function,
Fixing
the Quantity
Adding more
of one input
produces
less the more of that input you have
of(holding
Capital
and Varying the Quantity of
of Labor
and
Varying
the
Quantity
of
• MP
decreases
as
K
increases
N ∗ constant)
K
Capital • MPN decreases as N increasesLabour (holding K ∗ constant)
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
5-31
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
15
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Properties of the Production Function: Complements
The marginal product of a factor Adding
increasesCapital
with theIncreases
quantity ofthe
the Marginal
other factor
Marginal
Product of Labor Schedule
for
Product of Labor • MPN increases as K increases
he Representative
Firm •
MPK increases as N increases
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
16
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Firm’s Optimization Problem
• Firms are trying to maximize their profits
• Static Model: K is fixed
• Perfect Competition
▶ Firm is a price taker: wage w is given
• Monopsony (Future courses)
▶ Firm is a price maker: wage w is chosen
• Profits:
π = zF (K , N) − wN
17
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization: Perfect Competition
Assume perfect competition: Only choice is N
π = zF (K , N) − wN
Two methods for finding the optimal level of N
• Solve this graphically
• Solve this mathematically
18
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization: Graphical Approach
500
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization: Graphical Approach
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization: Graphical Approach
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Revenue, Variable Costs, and Profit
Profit Maximization:
Approach
MaximizationGraphical
Midterm
• MPN = w
• Graphical representation
22
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization: Mathematical Approach
Assume perfect competition: Only choice is N
π = zF (K , N) − wN
• The derivative tells us how profits changes when the firm changes the number of workers
∂π
= MPN − w
∂N
• The Marginal Product of Labour (MPN ) is the amount of output we can get from more
labour
• The wage w is the cost to hire more labour
23
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization: Mathematical Approach
• If MPN − w > 0
▶ Additional workers will produce more than the wage cost
▶ Want to hire more workers
• If MPN − w < 0
▶ The last worker produces less than the wage cost
▶ Want to hire fewer workers
• If MPN − w = 0
▶ The last worker produces the exact same as the wage cost
▶ Want to hire exactly this many workers!
▶ “Slope of the two function must be equal at the optimum”
• MPN is the slope of the production function
• w is the slope of the wage bill
24
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization: Mathematical Approach
General Mathematical Approach:
• Determine the objective function: The function you want to maximize
▶ Here the profit function
• Take the derivative of the objective function w.r.t. each choice made
▶ Here the only choice is the number of workers
• Set the derivative of the objective function equal to zero
▶ MPN − w = 0 =⇒ MPN = w
• Double check the optimum that you have found is a maximum
▶ Check second order condition (the second derivative)
25
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization Example
Consider a firm that produces with a Cobb-Douglas Production function:
Y = zK α N 1−α
Assume z = 2, K = 4, α = 21 , and w = 0.5
Solve for the profit-maximizing number of workers to hire
26
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Profit Maximization Example
π =zK α N 1−α − wN
∂π
=z(1 − α)K α N −α − w
∂N
0 =z(1 − α)K α N −α − w
wN α =z(1 − α)K α
z(1 − α)K α
Nα =
w
1
z(1 − α)K α α
N=
w

1
1
1
2(1 − 12 )4 2 2

N =
0.5
N =16
27
LaborModels
Demand
Micro-Founded
Curve
Firm Decisions
of the Profit-Maximizing Firm Consumer Decisions
Midterm
Labour Demand
28
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Limitations of this Model of Firm Decisions
What is this model missing?
• No differences in the quality or type of labour
• Investment in the capital stock
• Market Power
What is this model useful for?
• Think about firm decisions are affected by changes in:
▶ Wages
▶ Taxes
29
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Lecture 4: Static Model Consumers and Firms
• Micro-Founded Models
• Firm Decisions:
▶ Hire Labour
▶ Graphical Approach
▶ Mathematical Approach
• Consumer Decisions:
▶
▶
▶
▶
▶
Indifference curves
Budget constraints
Graphical Approach
Mathematical Approach
Exercises
30
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Decisions Intuition
A representative consumer:
• values consumption and leisure
• works and receives a wage
• takes time off and enjoys their leisure
• pays taxes
• receives dividends
Question: How does the consumer decide how much to work? How much to consume?
31
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
A Utility Function to Represent Preferences
U(c, ℓ)
• c is consumption of goods and services
• ℓ is any time spent enjoying leisure
• (c1 , ℓ1 ) is a consumption bundle.
• U(c1 , ℓ1 ) > U(c2 , ℓ2 ) ⇒ individual strictly prefers (c1 , ℓ1 ) to (c2 , ℓ2 ).
• U(c1 , ℓ1 ) = U(c2 , ℓ2 ) ⇒ individual indifferent between both consumption bundles.
32
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Indifference Curve
Definition: An indifference
curve connects
a set of points, representing consumption bundles,
Indifference
Curves among which the consumer is indifferent.
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Copyright © 2010 Pearson Educa8on Canada 5-5
- Monotone: the more, the better
▶ Implies indifference curves will slope down
- Convex: prefers averages to extremes
33
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Strict vs. Weak Monotonicity and Convexity
• Strictly monotone: More is always better
▶
∂U(·)
∂c
>0
• Weakly monotone: More is at least as good
▶
∂U(·)
∂c
≥0
• Strictly convex: Averages are always preferred
2 ℓ1 +ℓ2
▶ U(c1 , ℓ1 ) = U(c2 , ℓ2 ) < U( c1 +c
2 , 2 )
• Weakly convex: Averages are at least as good
2 ℓ1 +ℓ2
▶ U(c1 , ℓ1 ) = U(c2 , ℓ2 ) ≤ U( c1 +c
2 , 2 )
34
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
The Marginal Rate of Substitution (MRS)
The rate at which you would exchange two goods and remain indifferent
•
∂U(·)
∂c
= the marginal utility of consumption = MUc = Uc (c, ℓ)
•
∂U(·)
∂ℓ
= the marginal utility of leisure = MUℓ = Uℓ (c, ℓ)
• MRSℓ,c at point (c0 , ℓ0 )
MRSℓ,c =
∂U(·)
∂ℓ
∂U(·)
∂c
=
MUℓ
MUc
• The MRSℓ,c is the negative of the slope of the indifference curve at a particular
consumption bundle (c0 , ℓ0 ).
35
Micro-Founded Models
Firm Decisions
Consumer Decisions
Properties of Indifference Curves Midterm
The Marginal Rate of Substitution (MRS)
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Copyright © 2010 Pearson Educa8on Canada 5-6
• Convex: diminishing MRSℓ,c
36
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
The Time Constraint
• The consumer has a fixed amount of time h
• The consumer can choose to spend this time:
▶ Working N s
▶ Enjoying leisure ℓ
h = ℓ + Ns
37
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
The Budget Constraint
• w : Wage per unit of time
▶ Consumer is a price taker: Cannot choose wage
▶ Units of consumption good
• π: Dividends
▶ Profits of the firm
• T : Taxes
• c: Consumption
c = wN s + π − T
38
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
The Budget Constraint
c = wN s + π − T
c = w (h − ℓ) + π − T
c = −w ℓ + wh + π − T
• w , π, T , and h are all given
• c and ℓ are chosen
•
dc
dℓ
= −w ; The slope of the budget line
▶ This is the rate at which the labour market will transform leisure into consumption
• ↑ ℓ ⇒↓ c and ↓ ℓ ⇒↑ c
39
Micro-Founded Models
Firm Decisions
Consumer Decisions
The BudgetRepresentative
Constraint: (π − T ) <Consumer’s
0
Midterm
Budget Constraint (T > π)
c = −w ℓ + wh + π − T
40
Micro-Founded Models
Firm Decisions
TheRepresentative
Budget Constraint: Consumer’s
(π − T ) > 0
Constraint (T < π)
Consumer Decisions
Budget
Midterm
c = −w ℓ + wh + π − T
41
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Lecture 4: Static Model Consumers and Firms
• Micro-Founded Models
• Firm Decisions:
▶ Hire Labour
▶ Graphical Approach
▶ Mathematical Approach
• Consumer Decisions:
▶
▶
▶
▶
▶
Indifference curves
Budget constraints
Graphical Approach
Mathematical Approach
Exercises
42
Decisions
Consumer Firm
Optimization
Micro-Founded Models
Consumer Decisions
Midterm
Consumer Optimization: Graphical Approach
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada 1. Point J: inside the budget set ⇒ cannot be optimal
5-16
▶ You can afford more
▶ Monotone preferences: You prefer more of both goods
43
Decisions
Consumer Firm
Optimization
Micro-Founded Models
Consumer Decisions
Midterm
Consumer Optimization: Graphical Approach
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada 2. Point F : MRSℓ,c > w
5-16
▶ You are willing to give up more consumption for a unit of leisure than your wage
▶ E.g. MRSl,c = 2 and w = 1
44
Decisions
Consumer Firm
Optimization
Micro-Founded Models
Consumer Decisions
Midterm
Consumer Optimization: Graphical Approach
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada 3. Point E : MRSℓ,c < w
5-16
▶ You are willing to give up less consumption for a unit of leisure than your wage
▶ E.g. MRSl,c = 0.5 and w = 1
45
Decisions
Consumer Firm
Optimization
Micro-Founded Models
Consumer Decisions
Midterm
Consumer Optimization: Graphical Approach
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada 4. Point H: MRSℓ,c = w ; this is optimal.
5-16
▶ The amount of consumption you are willing to give up is exactly equal to your wage
▶ E.g. MRSℓ,c = 1 and w = 1
46
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Lecture 4: Static Model Consumers and Firms
• Micro-Founded Models
• Firm Decisions:
▶ Hire Labour
▶ Graphical Approach
▶ Mathematical Approach
• Consumer Decisions:
▶
▶
▶
▶
▶
Indifference curves
Budget constraints
Graphical Approach
Mathematical Approach
Exercises
47
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization: Setting Up the Mathematical Approach
• Preferences:
U(c, ℓ)
• Budget constraint:
c = −wl + wh + π − T
• What c and ℓ will maximize preferences?
▶ c = ∞ and ℓ = h will maximize preferences
▶ But this is unaffordable: it violates the budget constraint
• Question: How can we choose c and ℓ to maximize preferences while making sure the
budget constraint holds?
48
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem
max f (x1 , x2 ) = x1 x2
x1 ,x2
subject to
x1 + 4x2 = 16
where:
• f (x1 , x2 ) is the objective function
• x1 + 4x2 = 16 is the constraint
• x1 , x2 are the choice variables
49
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem: Lagrangian
Construct and maximize the Lagrangian function:
max L = x1 x2 − λ(x1 + 4x2 − 16)
x1 ,x2 ,λ
• Lagrangian gives us the ability to maximize the objective function
▶ While also penalizing us for exceeding the constraint
• λ is the Lagrange multiplier
▶ It tells us how much larger the objective function would be if we could relax the constraint
50
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem
The necessary first-order conditions (FOC) are:
∂L
• ∂x
=0
1
•
∂L
∂x2
=0
•
∂L
∂λ
=0
51
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem
max L = x1 x2 − λ(x1 + 4x2 − 16),
x1 ,x2 ,λ
52
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem
max L = x1 x2 − λ(x1 + 4x2 − 16),
x1 ,x2 ,λ
•
∂L
∂x1
= x2 − λ = 0
▶ λ = x2
52
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem
max L = x1 x2 − λ(x1 + 4x2 − 16),
x1 ,x2 ,λ
•
∂L
∂x1
= x2 − λ = 0
∂L
∂x2
= x1 − 4λ = 0
▶ λ = x2
•
▶ λ = 14 x1
52
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem
max L = x1 x2 − λ(x1 + 4x2 − 16),
x1 ,x2 ,λ
•
∂L
∂x1
= x2 − λ = 0
∂L
∂x2
= x1 − 4λ = 0
▶ λ = x2
•
▶ λ = 14 x1
•
∂L
∂λ
= −(x1 + 4x2 − 16) = 0
▶ x1 + 4x2 = 16
52
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
General Constrained-Optimization Problem
From the first two:
1
x2 = λ = x1
4
Substituting in to the third equation:
x1 + 4
1
x1 =16
4
2x1 =16
x1 =8
Therefore:
x2 = 2
λ=2
53
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization: Mathematical Approach
• Objective function is the preferences:
1
1
u(c, ℓ) = c 2 ℓ 2
• Constraint is the budget constraint:
c = w (h − ℓ) + π − T
• c and ℓ are the choice variables
• Our maximization problem is then:
1
1
max u(c, ℓ) = c 2 ℓ 2
c,ℓ
subject to
c = w (h − ℓ) + π − T
54
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization: Mathematical Approach
Assume that w = 1, h = 24, and π − T = 0. Then,
1
1
max L = c 2 ℓ 2 − λ(c − 24 + ℓ)
c,ℓ,λ
1
1
•
∂L
∂c
= 12 c − 2 ℓ 2 − λ = 0
•
∂L
∂ℓ
= 12 c 2 ℓ− 2 − λ = 0
•
∂L
∂λ
= −(c − 24 + ℓ) = 0
1
1
55
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization: Mathematical Approach
From the first two FOCs:
1 −1 1
1 1 1
c 2 ℓ 2 =λ = c 2 ℓ− 2
2
2
1
− 12
− 12 21
2
c ℓ =c ℓ
1
1
c − 2 ℓ =c 2
ℓ =c
Using the third FOC:
c = 12 = ℓ
λ=
1
2
56
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization Example
Preferences are:
U(c, ℓ) = log(c) + Aℓ
and assume that w = 300, h = 1, π = 25, and T = 75
Solve for the optimal amount of consumption and leisure.
57
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization Example
The Lagrangian is:
L = log(c) + Aℓ − λ(c − w (h − ℓ) − π + T )
Taking the derivatives:
∂L 1
= −λ
∂c c
∂L
=A − λw
∂ℓ
∂L
= − (c − w (h − ℓ) − π + T )
∂λ
58
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization Example
Setting the derivatives equal to zero:
1
0= −λ
c
0 =A − λw
0 = − (c − w (h − ℓ) + π − T )
Then doing some algebra:
1
0= −λ
c
1
λ=
c
0 =A − λw
A
λ=
w
59
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Consumer Optimization Example
1
A
=λ =
c
w
w =Ac
w
=c ∗
A
Using the budget constraint:
c ∗ = w (h − ℓ∗ ) + π − T
w
= w (h − ℓ) + π − T
A
w
w ℓ = wh + π − T −
A
π−T
1
∗
ℓ =h+
−
w
A
60
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Lecture 4: Static Model Consumers and Firms
• Micro-Founded Models
• Firm Decisions:
▶ Hire Labour
▶ Graphical Approach
▶ Mathematical Approach
• Consumer Decisions:
▶
▶
▶
▶
▶
Indifference curves
Budget constraints
Graphical Approach
Mathematical Approach
Exercises
61
Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Exercise 1: A Change in π or T
An Increase in π − T for the Consumer.
Consider an increase in π (or a decrease in T )
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• More is available at ℓ = h (point J)
• The slope of the budget line remains unchanged at w
• Both c and ℓ increase (as expected since both are normal goods).
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Income and Substitution Effects
• We can decompose the effect changes in this model into two effects:
▶ Income Effect: Measures the change in the consumption bundle from income changing with
prices fixed
▶ Substitution Effect: Measures the change in the consumption bundle from changing
relative prices, holding utility fixed
• When π or T changes, there is only an income effect
• There is no substitution effect because the relative prices of consumption c and leisure w
do not change
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Increase
Micro-Founded Models
inFirm
theDecisions
Real Wage Rate—
Consumer Decisions
Income and Substitution Effects
Exercise 2: An Increase in the Wage w
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada • Initially, we are at point F
• The relative price of leisure is w
• The price of consumption is 1
Midterm
5-23
64
Increase
Micro-Founded Models
inFirm
theDecisions
Real Wage Rate—
Consumer Decisions
Income and Substitution Effects
Exercise 2: An Increase in the Wage w
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada Midterm
5-23
1. Substitution effect (change relative prices, but keep individuals at the same utility level).
The budget line rotates from AB to JK .
▶ ↑ w ⇒ leisure more expensive
▶ ⇒ substitute ℓ for c
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Increase
Micro-Founded Models
inFirm
theDecisions
Real Wage Rate—
Consumer Decisions
Income and Substitution Effects
Exercise 2: An Increase in the Wage w
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada Midterm
5-23
2. Income effect (The budget line shifts from JK to EB.
▶ ↑ w ⇒ individuals are wealthier
▶ ⇒↑ ℓ and ↑ c
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Micro-Founded Models
Increase
Consumer Decisions
inFirm
theDecisions
Real Wage Rate—
Substitution
Exercise 2: AnIncome
Increaseand
in the
Wage w Effects
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Copyright © 2010 Pearson Educa8on Canada Midterm
5-23
• c increases unambiguously
• ℓ is ambiguous depending on the strength of the income and substitution effects
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Labour Supply
• N s (w ) = h − ℓ(w )
Labor Supply Curve • ℓ(w ) : ambiguous
• Assume that the substitution effect dominates the income effect
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Copyright © 2010 Pearson Educa8on Canada 5-24
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Normal Good
• Normal Good: if the quantity demanded increases as income increases
• Inferior Good: if the quantity demanded decreases as income increases
1
1
• The assumption of Cobb-Douglas preferences U(c, ℓ) = c 2 ℓ 2 implies that c and ℓ are
both normal goods
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Limitations of this Model of Consumer Decisions
What is this model missing?
• Some workers cannot choose their hours
• Some workers can bargain over their wages
• Some workers like working
• Workers save
What is this model useful for?
• Think about consumer decisions are affected by changes in:
▶ Wages
▶ Profits
▶ Taxes
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Lecture 4: Static Model Consumers and Firms
• Micro-Founded Models
• Firm Decisions:
▶ Hire Labour
▶ Graphical Approach
▶ Mathematical Approach
• Consumer Decisions:
▶
▶
▶
▶
▶
Indifference curves
Budget constraints
Graphical Approach
Mathematical Approach
Exercises
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Micro-Founded Models
Firm Decisions
Topics
Consumer Decisions
1
Introduction to Macroeconomics
Williamson Text
Chapters 1,2,3
2
3
Economic Growth
Agriculture (Malthus) and Capital (Solow)
Convergence and Human Capital
Chapter 7
Chapter 8
4
5
Static Model
Consumers and Firms
Governments and Labour Market Equilibrium
Chapter 4
Chapter 5
6
7
Dynamic Model
Consumption-Savings
Imperfect Credit Markets
Chapter 9
Chapter 10
8
Investment and General Equilibrium
Chapter 11
Midterm
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Progress So Far:
Completed:
• Lecture 1, 2, 3 and 4
• Read Williamson Chapters 1, 2, 3, 7, and 8
• Solved Problem Set 1, 2, and 3
To Do:
• Read Williamson Chapter 4
• Solve Problem Set 4
• Make Synthesized Notes
Next Up: Static Model: Government and Equilibrium
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Midterm Exam Logistics
• Scheduled on:
Monday October 16th during class time
• We will be in our normal lecture hall
▶ Sec 001: SSC 2032
▶ Sec 002: UCC 41
• You will need:
▶ Pencil or pen
▶ Non-graphing Non-programmable calculator
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Micro-Founded Models
Firm Decisions
Consumer Decisions
Midterm
Midterm Structure
• Counts for 20% of your course grade
• You will have 1 hour and 30 minutes
• There will be three questions
▶ They will look very similar to problem set questions
▶ Please do the problem sets!
• There is a practice midterm on OWL
▶ Practice doing it timed and without your notes
• Covers all of the course material
▶ Lectures 1, 2, 3, and 4
▶ Williamson Chapters: 1, 2, 3, 7, 8, and 4
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