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.
Understanding Macroeconomics IS-LM, Solow, New Keynesian
The goods market relationship comes from a spending feedback loop. When households receive more income, they usually spend part of it. That spending becomes income for someone else.
The final change in output can therefore be larger than the first change in government purchases or taxes. Its size depends on how much extra income people save, pay in taxes, or use to buy imports. Investment is especially important because firms compare the expected return from new equipment or buildings with the cost of borrowing.
A rise in interest rates can cancel part of a fiscal expansion by discouraging this investment. This effect is called crowding out.
The money market relationship shows why the response to policy is not fixed. People want money for everyday purchases and as a safe liquid asset. If income rises, more transactions take place, so money demand tends to rise.
With a fixed money supply, interest rates may need to increase to make people willing to hold less money. In a severe recession, interest rates may already be very low. Households and banks may then prefer to hold extra cash rather than spend or lend it.
Monetary policy can become weaker in this situation, while fiscal policy may have a larger effect. Real economies add banks, foreign trade, uncertainty, and changing expectations, so the model is a useful map rather than a full prediction machine.
The Solow model separates a temporary rise in living standards from permanent growth. Saving more creates more machines, roads, and factories per worker. At first this can raise output per worker quickly.
Later, each additional unit of capital adds less output than the previous one. Some investment must replace worn out capital. More workers and better technology mean that capital must be spread more widely.
This is why an economy can reach a stable capital level even while total output keeps growing. Sustained growth in output per person ultimately depends on improvements in technology, skills, organization, and knowledge. Countries with less capital may grow faster when they adopt existing technologies, though weak institutions or poor education can block that catch up.
New Keynesian analysis focuses on the fact that many prices and wages do not change immediately. Firms often set prices for a period of time. Workers may have contracts.
Because of this rigidity, a fall in demand can reduce production and employment before prices fall much. Inflation depends partly on what firms and households expect future inflation to be. If they expect high inflation, workers seek larger wage increases and firms raise prices sooner.
A supply disruption, such as an energy price jump, can raise inflation even when demand is weak. Central banks must then weigh the cost of reducing inflation against the cost of lower output and employment.
When studying these frameworks, first identify the time horizon. Demand policy matters most in the short run, while capital, productivity, and population matter over decades. Next, track the direction of each effect before trying to memorize diagrams.
Ask whether a change shifts a relationship or causes movement along it. Keep nominal values separate from real values, especially when inflation changes purchasing power.
Finally, state assumptions clearly. Fixed prices, a closed economy, stable expectations, or an unchanged money supply can make a classroom result clean, but changing any one of these assumptions can change the outcome.