## Macroeconomics Study Guides

Keep the following two comprehensive study guides handy throughout your macroeconomics course study. They provide brief oulines for many of the major macroeconomics topics studied in this course and can help prepare you for your final economics exams.

### Principles of Macroeconomics Lecture Notes

#### The Production Function

• GDP (Y) is produced with capital (K) and labor (N):

$\text{Y = A F(K,N)}$

where $A$ is Total Factor Productivity (TFP)

= an index of efficiency in the use of inputs (technology)

• Sometimes, I will modify the production function as follows:

$\text{Y = A F(K,N, other inputs)}$

where other inputs include energy/oil!

• Realistic Example is a Cobb Douglas function for F(.):

$Y =A \, K^{a}N^{1-a}$

with $0$< $α$ < $1$

#### Measurement

• Y is GDP (it is measured in dollars). As noted above, we want to measure Y in "real" terms.<<you should know what this means from lecture 2>>.
• For our Cobb Douglas production function, N is measured in number of workers and K in dollars:

– K often is measured as the replacement cost of capital

– N often is measured in number of workers

• N can also be measured using
total hours worked = number of workers × hours per worker
• Wage differentials can help to measure "effective labor supply", taking into account "skill" differentials.

N.B.: sometimes we will use N to denote total population (e.g. income per capitaY/N)

#### Graphical Representation 1

• Hold A and N constant (at levels A* and N*)
• Graph Y as a function of K

1. As K increases Y increases (the curve is upward-sloping)

2. As K increases the marginal increase in production decreases (the curve becomes flatter as K increases)

#### Graphical Representation 2

• Hold A and K constant (at levels A* and K*)
• Graph Y as a function of N

1. As N increases Y increases (the curve is upward-sloping)

2. As N increases the marginal increase in production decreases (the curve becomes flatter as N increases)

#### Aggregate Production Function: Fact 1

1. Constant Returns to Scale

FACT 1: If you double the inputs, you double the output!

$\text{2Y = AF(2K,2N)}$

Cobb-Douglas:

$2Y = A (2K)^{α} \, (2N)^{1- α}= 2A \, K^{a}N^{1- α}$

CRUCIAL: $\text{α + (1- α) = 1}$!

#### Aggregate Production Function: Fact 2

2. Diminishing Returns to N and K

Define $\text{MPN = Marginal Product of Labor = dY/dN}$

Define $\text{MPK = Marginal Product of Capital = dY/dK}$

FACT 2: MPN decreases with N and MPK decreases with K

Cobb-Douglas:

• $\text{MPN = (1- α) A (K/N)}^{a}$

Fixing A and K, MPN falls when N increases

• $\text{MPK = α A (N/K)}^{1-a}$

Fixing A and N, MPK falls when K increases

#### Aggregate Production Function: Fact 3

3. Complementarities between A, K and N

FACT 3: The higher the level of capital (or technology), the higher the marginal product of labor (and symmetrically for capital!)

Cobb-Douglas:

• $\text{MPN = (1- α) A (K/N)}^{a}$

Increasing A or K, increases MPN

• $\text{MPK = α A (N/K)}^{1-a}$

Increasing A or N, increases MPK

#### Aggregate Production Function: Fact 4

4. Elasticities and Income Shares

• Elasticity is the percentage increase in Y (dependent variable) resulting from a

1% increase in X (independent variable), everything else constant

$\eta_{\mathrm{N}}=\% \text { change in } \mathrm{Y} / \% \text { change in } \mathrm{N}=(\mathrm{d} \mathrm{Y} / \mathrm{Y}) /(\mathrm{d} \mathrm{N} / \mathrm{N})=\mathrm{MPN} /(\mathrm{Y} / \mathrm{N})$

FACT 4: Labor Elasticity ~.7

Capital Elasticity ~.3

Cobb-Douglas:

• $\eta_{N}=(1-\alpha) \text { and } \eta_{K}=\alpha$

That's why we pick $\text{α =.3}$ !!

• Share of labor income out of total GDP is about 70%
Share of capital income out of total GDP is about 30%

#### Two Notions of Productivity

• $\text{Labor Productivity = Y/N = A (K/N)}^{3}$

Driven by A and K/N

• $\text{Total Factor Productivity (TFP) = Y/F(K,N) = A}$

Basically TFP is a 'catch-all' for anything that effects output other than K and N.

• Workweek of labor and capital
• Quality of labor and capital
• Regulation
• Infrastructure
• Specialization
• R&D, Innovation
• Strategy (Entrepreneurial methods/new management techniques)

• Some of the above tend to make TFP procyclical (capital utilization)

(Definition of Procyclical: Variable increases when Y is high, decreases when Y is low)

Simple examples (in words)

1. Technology: "It costs FedEx $2.40 to track a package for a customer who calls by phone, but only$0.04 for one who visits its website", says Rob Carter, the firm's technology boss.
2. Technology: "Airline kiosks reduce costs of boarding to less than a third".
3. Management: Southwest’s oil hedging. Estimated oil price paid by SW: $31. United:$56.
4. Infrastructure: Imagine what it takes to buy intermediate inputs from a different region with roads like in Nigeria.

#### Measure of Labor productivity

##### Productivity Levels

United States = 100

Country GDP per capita
Labour productivity

Per person employed
Per hour worked
1995 2003 1995 2003 1995 2003
United States
100 100 100 100 100 100
Euro area
72 70 84 77 95 89
Germany
77
70 81 73  97 90
France 75 74 83 88 108 107
Italy 75 70
93 80 104 88
Spain 57 62 78 73 83 75
Netherlands 78 78 80 73 107
98
Belgium 78 76 98 92 111 106
Austria 84 79 81 74
98 87
Greece 47
52 64 70 61 64
Portugal 47 49 47 49
47 51
Finland 69 72 81 76 87 80
Ireland 64 87 86
92 86 99
Japan
81 74 82 69 71 69
United Kingdom
72 77 76 79 81 83
Canada 80 87 89 86 92 86
Sweden 77 75
70 71 80 86
Denmark 81 80 76 75 92 89
Norway 86 96 84 92 110 123
Iceland 81  76  83 74  84  73