Economics Chapter 9: Productivity, Growth, and Development

[Ch9] Y

Real GDP — the total inflation-adjusted output (and income) of a country. The macro variable of focus for long-run growth.

[Ch9] Pop

Population — the total number of people in a country.

[Ch9] L

The number of workers (laborers) — people who are actually working.

[Ch9] Y/Pop (real GDP per capita)

Real GDP divided by population. Best available measure of the average person's living standards.

[Ch9] Y/L (real GDP per worker)

Real GDP divided by the number of workers. This is labor productivity.

[Ch9] K

Physical capital — man-made goods used to produce other goods (machines, factories, cameras, production trucks).

[Ch9] H

Human capital — the knowledge, skills, and education embodied in workers (a technician learning to use a machine).

[Ch9] T (in Ch9!)

The state of technology (augmented reality, Hawk-Eye tech). CAREFUL: in Ch10, T means taxes.

[Ch9] K/L

Physical capital per worker.

[Ch9] H/L

Human capital per worker.

[Ch9] Total factor productivity (TFP)

The amount of output that can be produced from a given amount of factor inputs (labor + physical capital). Measures technology's contribution to productivity growth (factor inputs held constant).

[Ch9] Why real GDP per capita and not nominal GDP?

"Per capita" = per person. Nominal GDP is not adjusted for inflation — it can rise just because prices rose. Real GDP per capita rises only when real output per person grows, so it best tracks living standards.

[Ch9] RULE: Population grows faster than real GDP → ?

Real GDP per capita (Y/Pop) must be falling — living standards fall.

[Ch9] RULE: Workers grow faster than real GDP → ?

Productivity (Y/L) must be falling, since %Δ(Y/L) = %ΔY − %ΔL.

[Ch9] TRAP: Pop grows faster than Y. Does Y/L fall?

Not necessarily! You only know Y/Pop falls. Without info on how the number of workers changed, Y/L is unknown.

[Ch9] What has long-run economic growth mostly depended on?

Rising productivity (real GDP per worker) — not low unemployment, not population growth.

[Ch9] TRAP: Does a bigger labor force raise productivity?

No — productivity is real GDP per worker. More workers alone (same output) lowers Y/L.

[Ch9] If Y grows 6% and workers grow 1%, what happens to productivity?

Grows ≈ 5% (6% − 1%). %Δ(Y/L) = %ΔY − %ΔL.

[Ch9] If Y grows 6% and population grows 6.5%, what happens to living standards?

Real GDP per capita falls ≈ 0.5% — population outpaced output.

[FORMULA - ON SHEET] Rule of 70 (doubling time)

Doubling time (years) = 70 / growth rate (%). Use the growth rate as a whole number: 7% growth → 70/7 = 10 years.

[FORMULA - ON SHEET] Rule of 70 (growth rate)

Growth rate (%) = 70 / doubling time (years) — the on-sheet formula rearranged. E.g., doubles in 20 years → 3.5% growth.

[FORMULA - NOT ON SHEET] Y/Pop identity

Y/Pop = (Y/L) × (L/Pop). Real GDP per capita = productivity × the share of population working.

[FORMULA - NOT ON SHEET] Growth of productivity

%Δ(Y/L) ≈ %ΔY − %ΔL (course shortcut). Percent change of a fraction ≈ % change of numerator − % change of denominator.

[FORMULA - NOT ON SHEET] Growth of living standards

%Δ(Y/Pop) ≈ %ΔY − %ΔPop (course shortcut).

[FORMULA - NOT ON SHEET] Percent change (growth rate)

% change = (new − old) / old × 100. E.g., real GDP rose from 86,400 to 100,000 → (13,600/86,400) × 100 ≈ 15.7%.

[FORMULA] Δ (delta)

The symbol for "change in". %Δ = percent change.

[FORMULA] X (in FV/PV formulas)

The amount of money. In FV: the amount deposited today. In PV: the future payment you will receive or pay.

[FORMULA] r (in FV/PV formulas)

The interest (discount) rate per period, entered as a DECIMAL: 5% → 0.05. EXCEPTION: the Rule of 70 uses the growth rate as a whole number (7 means 7%).

[FORMULA] N (in FV/PV formulas)

The number of years (periods) the money compounds or is discounted.

[FORMULA - NOT ON SHEET] Time to quadruple (4×)

4× requires TWO doublings: time = 2 × doubling time. (8× requires three doublings.)

[FORMULA - NOT ON SHEET] Doubling comparison trick

Two doublings = 4×; three doublings = 8×. A country growing at 2% for 35 years doubles once ($10k→$20k); at 4% it doubles twice ($10k→$40k).

[Ch9] Diminishing returns to physical capital

Each additional unit of capital per worker raises productivity by LESS than the previous unit (productivity gains: 3%, 2%, 1%...). Assumption: other inputs (H/L, T) held constant.

[Ch9] Doubling physical capital → productivity?

Less than doubles, because of diminishing returns.

[Ch9] Cobb-Douglas production function

Y/L = T × (K/L)^0.4 × (H/L)^0.6. You will NOT be asked to compute it — know its graph and meaning.

[Ch9] Aggregate production function: axes

Vertical axis: real GDP per worker (Y/L). Horizontal axis: physical capital per worker (K/L). Curve is upward-sloping and concave (flattens as K/L rises).

[Ch9] GRAPH RULE: Movement ALONG the curve (A → B)

Only K/L changes. T and H/L are fixed. This is NOT a shift.

[Ch9] GRAPH RULE: Shift UP of the curve (B → C)

T or H/L (or both) increase; K/L is fixed. The whole curve moves up.

[Ch9] GRAPH RULE: Shift DOWN of the curve

H/L or T falls — e.g., brain drain (educated workers leaving), corrupt government.

[Ch9] TRAP: B to C, no change in K/L. Must it be technology?

No — it could be better technology OR more human capital (or both). Don't ignore H.

[Ch9] TRAP: Destroyed physical capital (war destroys a power plant)

A movement DOWN-ALONG the curve (less K/L), not a shift of the curve.

[Ch9] Growth accounting

Quantifies how much of productivity growth is due to each factor: K, H, and T. E.g., productivity rose 50 total; K alone explains 20 of it → K's share = 20/50 = 40%; the shift explains 30/50 = 60%.

[Ch9] If productivity doubled in 10 years, the growth rate was...

7% (Rule of 70: 70/10).

[Ch9] Catch-up effect

Poor countries grow faster than rich ones: the same addition of capital is more productive where capital is scarce (diminishing returns work in reverse).

[Ch9] Convergence hypothesis

Relatively poor nations should have higher growth rates of real GDP per capita, so the income gap between poor and rich countries narrows over time.

[Ch9] Conditional convergence

Poor countries' faster growth is conditional on an educated workforce and the right environment to use available technology.

[Ch9] Government policies that FOSTER growth

Political stability; protection of property rights and intellectual property; infrastructure; education and basic research; savings and a well-functioning financial system; fair tax system; accessible financing.

[Ch9] Factors that HURT long-run growth

Hyperinflation and banking collapse (Argentina); coups and instability (Sudan); weak rule of law; excessive government intervention and licensing; corruption; business owners unable to get financing.

[Ch9] Growth + government: infrastructure example

China's high-speed rail build-out → infrastructure (+) growth.

[Ch9] Growth + government: education example

Vietnam's college enrollment rising 3% → 30% → education and basic research (+) growth.

[Ch9] Workers today more productive than in the past because...

They have more physical capital embodying better technology to work with.

[Ch9] Rising high school graduation rates are an increase in...

Human capital.

[Ch9] To acquire human capital, a person would...

LEARN something (learn to use a printing press) — not buy the machine (that's K), not sell output, not go into debt.

[Ch10-LF] C

Consumption spending (households).

[Ch10-LF] G

Government spending on goods and services.

[Ch10-LF] T (in Ch10!)

Taxes. CAREFUL: not technology like in Ch9.

[Ch10-LF] I

Investment spending — spending on NEW physical capital.

[Ch10-LF] r

The interest rate — the "price" in the loanable funds market (price of borrowing / return to saving).

[Ch10-LF] Q

Quantity of loanable funds (billions of dollars).

[FORMULA - NOT ON SHEET] National savings

S = Y − C − G. What the country saves in total. NOT the same as government savings.

[FORMULA - NOT ON SHEET] Private savings

Y − T − C. What private individuals (households) save out of after-tax income.

[FORMULA - NOT ON SHEET] Government (public) savings

T − G. Also called the budget balance. Negative = budget deficit; positive = budget surplus.

[FORMULA - NOT ON SHEET] National savings = ?

National savings = private savings + government savings. E.g., 8 + 2 = 10.

[FORMULA - NOT ON SHEET] Savings-investment spending identity (closed economy)

Investment spending = national savings (I = Y − C − G). In a closed economy, all investment must be financed by domestic saving.

[FORMULA - NOT ON SHEET] Finding T from the budget balance

Budget balance = T − G, so T = G + budget balance. E.g., G = 10, balance = 2 → T = 12.

[Ch10-LF] Worked example: Y=50, C=30, G=10, budget balance=2

T = 12; private savings = 50−12−30 = 8; government savings = 2; national savings = 10 = investment spending.

[Ch10-LF] Worked example: Y=20, C=14, G=3, budget balance=−1

T = 2; private savings = 20−2−14 = 4; government savings = −1 (deficit); national savings = 3 = investment spending.

[Ch10-LF] What counts as investment spending (macro)?

Actions that create NEW physical capital: a developer building 80 new houses; buying a new truck for a business.

[Ch10-LF] TRAP: Buying Tesla shares is NOT investment spending

It is a financial investment — no new physical capital is created.

[Ch10-LF] TRAP: Paying tuition with a student loan is NOT investment spending

It is investment in HUMAN capital — no new physical capital is created.

[Ch10-LF] Demand side of the loanable funds market

BORROWERS — anyone who takes out a loan is on the demand side: firms financing investment spending (the course's main focus), the government covering deficits, households borrowing (credit cards, consumer loans).

[Ch10-LF] Supply side of the loanable funds market

Savers: households saving for retirement or emergencies, plus foreign savers. Supply = saving.

[Ch10-LF] Why does the demand curve slope DOWN?

The interest rate is the price of borrowing — quantity of funds demanded is lower when the price (r) is higher.

[Ch10-LF] Why does the supply curve slope UP?

A higher interest rate is a bigger reward for saving, so quantity supplied rises with r.

[Ch10-LF] GRAPH RULE: Loanable funds market axes

Vertical: interest rate (r). Horizontal: quantity of loanable funds. S slopes up, D slopes down; equilibrium where they cross.

[Ch10-LF] GRAPH RULE: Shortage (r below r*)

Quantity demanded > quantity supplied. Borrowers compete for scarce funds → pressure for r to RISE toward equilibrium.

[Ch10-LF] GRAPH RULE: Surplus (r above r*)

Quantity supplied > quantity demanded. Savers compete to attract borrowers → pressure for r to FALL toward equilibrium.

[Ch10-LF] GRAPH RULE: r adjusts to restore equilibrium — shift or movement?

A MOVEMENT ALONG the D and S curves toward the equilibrium point. Curves do not shift.

[Ch10-LF] At equilibrium, funded projects have a rate of return that is...

At least r* (≥ the equilibrium interest rate). Projects returning less than r* don't get funded/borrowed.

[Ch10-LF] When does a firm borrow for a project?

Only if the project's rate of return is at least the interest rate. Return > r → profitable, borrow. Return < r → will NOT borrow. Return = r → break-even (indifferent).

[Ch10-LF] Saver who needs at least 12% but equilibrium r = 10%

Will NOT save in this market (savers only earn the equilibrium rate).

[Ch10-LF] GRAPH RULE: Demand shifts RIGHT

Business optimism/confidence (AI excitement, equipment upgrades), government budget deficit, consumers/investors more eager to borrow. → r up, Q up.

[Ch10-LF] GRAPH RULE: Demand shifts LEFT

Uncertainty or pessimism about investment returns (e.g., developer bankruptcy scares firms). → r down, Q down.

[Ch10-LF] GRAPH RULE: Supply shifts RIGHT

More saving at every r: retirement-saving campaigns, a larger share of savers in the population, foreign capital inflows. → r down, Q up.

[Ch10-LF] GRAPH RULE: Supply shifts LEFT

Less saving: higher taxes on savings/interest earnings, more retirees in the population, higher consumption. → r up, Q down.

[Ch10-LF] GRAPH RULE: 4 quick predictions

D right → r up, Q up. D left → r down, Q down. S right → r down, Q up. S left → r up, Q down.

[Ch10-LF] GRAPH RULE: r up AND Q down → what happened?

Supply decreased (shifted left). r down + Q up → supply increased. r up + Q up → demand increased. r down + Q down → demand decreased.

[Ch10-LF] GRAPH RULE: Both curves shift

One outcome is certain, the other is uncertain. E.g., D right + S left → r rises for sure, Q uncertain. D right + S right → Q rises for sure, r uncertain.

[Ch10-LF] Crowding out

A government budget deficit shifts demand right → r rises → PRIVATE investment spending falls (private borrowers are squeezed out).

[Ch10-LF] Crowding out: how to compute it

Crowd out = private borrowing BEFORE − private borrowing AFTER. E.g., $500B before → $400B after → $100B crowded out.

[Ch10-LF] Deficit scenario: total vs government vs private borrowing

New total borrowing = new equilibrium Q. Government gets the deficit amount; private borrowing = new total − deficit. E.g., total $600B, deficit $200B → private $400B.

[Ch10-LF] GRAPH RULE: Size of the deficit on the graph

The horizontal distance between the old demand curve D and the new demand curve D2.

[Ch10-LF] RULE: Budget deficit → what happens? (supply fixed)

The deficit shifts demand right → r rises, TOTAL borrowing rises, and private investment spending is crowded out. The government becomes a borrower in the market.

[Ch10-LF] War + higher household saving at the same time

D right (government borrowing) + S right (more saving) → quantity rises for sure, interest rate uncertain.

[Ch10-LF] Mineral discovery: optimism + foreign savings inflow

D right + S right → equilibrium quantity increases for sure; interest rate uncertain.

[Ch10-LF] Is a stock purchase on the NYSE investment spending?

No — it is a secondary-market financial transaction, not macro investment spending.

[Ch10-FIN] Asset

Whatever you OWN (savings account, loan you made, checking balance).

[Ch10-FIN] Liability

Whatever you OWE (mortgage payments, credit card balance, student loan for the borrower).

[Ch10-FIN] Loan: asset or liability?

A loan is a LIABILITY to the borrower and an ASSET to the lender (bank).

[Ch10-FIN] Financial intermediary

An institution that channels savings to borrowers — INDIRECT finance. Commercial banks take deposits and make loans; mutual funds pool savers' money into portfolios. Not the same as a financial market.

[Ch10-FIN] Financial market

A place where savers DIRECTLY provide funding to those raising money (NYSE, bond markets). Direct finance.