This cheat sheet summarizes three core macroeconomic frameworks used to analyze output, interest rates, growth, inflation, and stabilization policy. IS-LM explains short-run equilibrium in goods and money markets. The Solow model explains long-run growth through capital accumulation, population growth, and technology.
The New Keynesian model connects inflation dynamics, output gaps, and monetary policy in modern macroeconomics.
The most important ideas are equilibrium conditions, comparative statics, and how policy shocks move key variables. IS-LM uses Y = C + I + G and M/P = L(Y, i) to study demand-side fluctuations. Solow uses k, y = f(k), and the steady-state condition s f(k) = (delta + n + g)k to study growth per effective worker.
New Keynesian analysis often uses an IS curve, a Phillips curve, and a policy rule such as i = r* + pi + phi_pi(pi - pi*) + phi_y y_gap.
Key Facts
- In the IS-LM model, the IS curve is goods market equilibrium: Y = C(Y - T) + I(i) + G, where higher interest rates usually reduce investment and output.
- The LM curve is money market equilibrium: M/P = L(Y, i), where higher income raises money demand and higher interest rates lower money demand.
- Expansionary fiscal policy, such as higher G or lower T, shifts the IS curve right and usually raises Y and i in the short run.
- Expansionary monetary policy, such as higher M, shifts the LM curve right and usually raises Y while lowering i in the short run.
- In the Solow model, capital per effective worker evolves according to delta k = s f(k) - (delta + n + g)k.
- The Solow steady state satisfies s f(k*) = (delta + n + g)k*, where investment per effective worker equals break-even investment.
- The New Keynesian Phillips curve can be written as pi = beta E(pi_next) + kappa y_gap + u, linking inflation to expected inflation, the output gap, and cost-push shocks.
- A simple Taylor rule is i = r* + pi + phi_pi(pi - pi*) + phi_y y_gap, and stability usually requires phi_pi greater than 1.
Vocabulary
- IS curve
- The set of output and interest rate combinations where planned spending equals actual output in the goods market.
- LM curve
- The set of output and interest rate combinations where real money supply equals real money demand.
- Steady state
- A long-run position in the Solow model where capital per effective worker is constant because investment equals break-even investment.
- Output gap
- The difference between actual output and potential output, often measured as y_gap = Y - Y_potential or as a percentage gap.
- Natural rate of interest
- The real interest rate consistent with output at potential and stable inflation when temporary shocks are absent.
- Phillips curve
- A relationship describing how inflation depends on expected inflation, real economic activity, and supply or cost shocks.
Common Mistakes to Avoid
- Confusing movements along a curve with shifts of a curve is wrong because a change in an axis variable causes movement, while a change in an outside factor shifts the whole curve.
- Treating nominal money M as the same as real money M/P is wrong because money market equilibrium depends on purchasing power, not just the number of currency units.
- Forgetting depreciation, population growth, and technology growth in the Solow break-even term is wrong because steady-state investment must cover (delta + n + g)k.
- Assuming a higher saving rate permanently raises growth in the basic Solow model is wrong because it raises the level of output per effective worker, not the long-run growth rate.
- Ignoring expectations in the New Keynesian Phillips curve is wrong because current inflation depends strongly on expected future inflation as well as the output gap.
Practice Questions
- 1 In an IS-LM model, suppose C = 100 + 0.8(Y - T), T = 100, I = 200 - 20i, and G = 150. Write the IS equation relating Y and i.
- 2 In a Solow model with s = 0.25, f(k) = k^0.5, delta = 0.05, n = 0.01, and g = 0.02, find the steady-state condition for k* and solve for k*.
- 3 Using pi = beta E(pi_next) + kappa y_gap + u, calculate pi when beta = 0.95, E(pi_next) = 2, kappa = 0.5, y_gap = 1, and u = 0.3.
- 4 Explain why a central bank following a Taylor rule with phi_pi less than 1 may fail to stabilize inflation after an inflation shock.