Glossary

Every key term across the study guides, with the chapter that introduces it

B

Balanced growth path (steady state) 🟢

The path on which per-capita capital and consumption are constant and aggregates grow at the population growth rate. (Chapter 3)

C

Co-state variable (λ) 🔵

The shadow price of the state variable: the current value of one more unit of capital. (Chapter 3)

Control variable 🟢

A jumpy variable chosen freely at each instant, such as consumption. (Chapter 3)

Current-value Hamiltonian 🔵

The function \(H = u(c)e^{nt} + \lambda[f(k) - nk - c]\) used to solve dynamic optimisation problems in continuous time. (Chapter 3)

D

Dynamic inefficiency 🔵

Oversaving: a capital stock above the golden rule, so everyone could consume more forever. Optimal saving in the NGM rules it out. (Chapter 3)

E

Elasticity of intertemporal substitution (σ) 🟢

How strongly consumption growth responds to the gap between the return on saving and impatience; \(\sigma = -u'(c)/(u''(c)c)\). (Chapter 3)

Elasticity of substitution (ε) 🔵

How easily capital can replace labour in production; below one, labour becomes more essential as the economy grows. (Chapter 3)

Euler equation (Keynes–Ramsey rule) 🟢

The optimality condition \(\dot c/c = \sigma[f'(k) - \rho]\): consumption grows when the return on saving exceeds the rate of time preference. (Chapter 3)

G

Golden rule 🟢

The capital stock that maximises steady-state consumption per capita, where \(f'(k_G) = n\). (Chapter 3)

I

Intertemporal budget constraint 🔴

The present value of lifetime consumption equals initial assets plus the present value of wages. (Chapter 3)

L

Labour share 🔵

The fraction of income paid to labour, \(wL/Y\); constant (\(= \alpha\)) with Cobb–Douglas technology. (Chapter 3)

M

Modified golden rule 🟢

The optimal steady-state capital stock, where \(f'(k^*) = \rho\); below the golden rule because \(\rho > n\). (Chapter 3)

N

No-Ponzi-game condition 🔴

The constraint that households cannot borrow forever to pay interest on earlier debt: \(\lim a_t e^{-(r-n)t} \ge 0\). (Chapter 3)

P

Phase diagram 🔵

A plot of the \((k, c)\) plane with the \(\dot k = 0\) and \(\dot c = 0\) loci and arrows showing the direction of motion in each region. (Chapter 3)

R

Rate of time preference (ρ) 🟢

How much less a household values consumption one instant later; the model requires \(\rho > n\). (Chapter 3)

Representative household 🟢

A single household standing in for the whole economy, valid when people respond similarly to incentives. (Chapter 3)

S

Saddle path 🔵

The unique trajectory that converges to the steady state; consumption jumps onto it and the economy then moves along it. (Chapter 3)

Saddle-path stability 🔴

A steady state with one stable and one unstable eigenvalue, which delivers a unique converging path when there is one jump variable. (Chapter 3)

State variable 🟢

A sticky variable that can change only gradually, such as the capital stock. (Chapter 3)

T

Transversality condition (TVC) 🔴

The optimality condition \(\lim_{t\to\infty} k_t\lambda_t e^{-\rho t} = 0\): never end with valuable capital that could have been consumed. (Chapter 3)