Macroeconomics Study Guides
Principles of Macroeconomics Lecture Notes
The Production Function
- GDP (Y) is produced with capital (K) and labor (N):
whereis Total Factor Productivity (TFP)
= an index of efficiency in the use of inputs (technology)
- Sometimes, I will modify the production function as follows:
- Realistic Example is a Cobb Douglas function for F(.):
with < <
- 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!
Aggregate Production Function: Fact 2
2. Diminishing Returns to N and K
FACT 2: MPN decreases with N and MPK decreases with K
Fixing A and K, MPN falls when N increases
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!)
Increasing A or K, increases MPN
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
FACT 4: Labor Elasticity ~.7
Capital Elasticity ~.3
That's why we pick!!
- 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
Driven by A and K/N
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
- 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)
- 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.
- Technology: "Airline kiosks reduce costs of boarding to less than a third".
- Management: Southwest’s oil hedging. Estimated oil price paid by SW: $31. United: $56.
- Infrastructure: Imagine what it takes to buy intermediate inputs from a different region with roads like in Nigeria.
Measure of Labor productivity
United States = 100
|Country||GDP per capita
|Per person employed
||Per hour worked