Chapter 2: Aggregate Demand and the Monetary Transmission Mechanism#

What makes an economy spend more today rather than save for tomorrow? And how does a central bank’s choice of a short-term interest rate pass through the whole economy to affect output, jobs, and inflation? In this chapter we build the core model of aggregate demand and show exactly how monetary policy works—from the central bank’s policy lever all the way to household spending and the price level.

The Big Picture#

Aggregate demand is the total amount of goods and services that households, firms, and the government want to buy at a given price level. The monetary transmission mechanism is the chain that connects the central bank’s chosen interest rate to these spending decisions. We start with the simplest piece of demand: how a single household decides to split its spending between today and tomorrow. That decision, when added up across millions of households, gives us the forward‑looking IS curve—a relationship between the output gap, expected future output, and the real interest rate. We then bring in the central bank, which follows a simple policy rule like the Taylor rule. Combining the two shows why a central bank must be strong enough to anchor inflation expectations, and why promises about future policy matter a lot. Finally, we look at labour market frictions and a welfare‑based loss function to see what the central bank should really care about, and we compare different intermediate targets such as nominal GDP and the price level.

How Households Decide Consumption Today and Tomorrow#

Imagine you receive some income today and expect more tomorrow. How much should you consume now and how much should you save? A rational household wants to smooth consumption—no one likes feast then famine. The key trade‑off: spending one extra dollar today gives immediate happiness, but saving that dollar lets you spend more tomorrow because you earn interest. The best plan balances the extra happiness today with the discounted extra happiness tomorrow, after accounting for the interest you earn.

Let be consumption today, be consumption tomorrow, the utility (happiness) from consuming, and the discount factor (how patient you are, between 0 and 1). If you save one unit, you get back units of real goods next period, where is the real interest rate. This balancing act gives us the intertemporal Euler equation:

Here stands for the expectation formed today about tomorrow’s situation. In plain words: the extra happiness you get from consuming a bit more today must equal the happiness you expect to get from that bit tomorrow, after discounting and adding the interest you earn by saving.

Intertemporal Euler equation: A condition that pins down how a household splits consumption between today and tomorrow by weighing the benefit of spending now against the reward of saving, which is the real interest rate.

To see what the interest rate does, imagine you are very impatient ( is small) and the real rate is low. The right‑hand side is small, meaning the future reward for saving isn’t very tempting. So you’d rather spend more today, which brings down today’s marginal utility, and save less for tomorrow. If the central bank raises the real interest rate, the right‑hand side gets bigger, so saving becomes more rewarding. You cut back today’s spending. This is how the central bank’s interest rate affects demand.

If we pick a simple utility function, like , the Euler equation becomes

This tells us that a higher real interest rate encourages saving and lowers consumption today. Adding up all households, we get the forward‑looking IS curve, which links the output gap to the real interest rate and expected future output.

📝 Section Recap: The Euler equation shows that households balance spending today against saving for tomorrow. The real interest rate is the key lever: a higher real rate makes saving more attractive and reduces current consumption.

From Consumption Plans to the IS Curve#

Let denote the logarithm of real output, and its natural level—the level that would occur if all prices and wages were completely flexible. The difference is the output gap. The forward‑looking IS curve links the output gap to the real interest rate:

Here is the nominal interest rate set by the central bank, is inflation between and , so is the expected real interest rate. The parameter captures how sensitive consumption is to the real rate—higher means households dislike large swings in consumption, so they adjust less. The term is the natural rate of interest, the real rate that would keep output at its natural level if all prices were flexible. It changes over time because of productivity shocks, shifts in patience, or fiscal policy.

Output gap: The percentage deviation of actual GDP from the level that would occur under fully flexible prices and wages, often called potential output. A positive gap means the economy is overheating; a negative gap means it is in a slump.

Natural rate of interest: The real interest rate that equates saving and investment when output is at its natural level and inflation is stable. Sometimes called .

Forward‑looking IS curve: A relationship showing that today’s output gap rises when people expect higher future output, and falls when the real interest rate is above its natural rate.

The IS curve is forward‑looking because today’s demand depends on expectations of tomorrow’s income. If households expect a boom next year ( is high), they feel wealthier and spend more today. The monetary transmission channel is clear: the central bank changes the nominal rate . Given expected inflation, this changes the real rate, which in turn moves the output gap. This is the demand side of the model.

📝 Section Recap: The forward‑looking IS curve shows that the output gap depends on expected future output and the gap between the current real interest rate and the natural rate, making expectations and interest‑rate policy central to aggregate demand.

How Central Banks Set Interest Rates: The Taylor Rule#

Central banks do not pick interest rates at random. A remarkably good description of actual policy is the Taylor rule, which says that the central bank adjusts its policy rate in response to inflation and the output gap:

The constant is the sum of the steady‑state real rate and the inflation target, and and are positive coefficients that measure how strongly the bank reacts. When inflation rises above target, the bank raises the nominal rate by more than one‑for‑one (typically ), which pushes the real rate up and cools demand. Similarly, a positive output gap calls for a higher rate.

Taylor rule: A simple policy prescription linking the central bank’s nominal interest rate to current inflation and the output gap, with coefficients that reflect the bank’s preferences.

The Taylor rule can be extended to respond to expected future inflation, or to include interest‑rate smoothing, but the core idea is the same: the central bank systematically leans against both inflation and output deviations.

Determinacy: Why Rules Anchor Inflation Expectations#

Combining the IS curve with a Taylor‑type rule gives a complete system. But not every rule works. Suppose the central bank fails to raise the nominal rate enough when inflation rises—say . In that case, higher inflation lowers the real interest rate, which stimulates demand and pushes inflation even higher. This self‑fulfilling spiral can lead to many possible paths for inflation and output, none uniquely pinned down. The economy can jump to a boom or bust simply because people believe it.

The Taylor principle says that to guarantee a unique stable equilibrium—determinacy—the nominal rate must rise more than one‑for‑one with inflation, . Intuitively, the real rate must rise when inflation rises, acting as a cooling force that brings inflation back to target. A central bank that follows this principle anchors inflation expectations: people know that any deviation from target will be met with a firm response.

Taylor principle: The requirement that the policy interest rate responds more than proportionally to inflation, ensuring that the real rate moves in the same direction as inflation, which eliminates self‑fulfilling inflationary spirals.

📝 Section Recap: A monetary policy rule must satisfy the Taylor principle—raising the nominal rate by more than the increase in inflation—to give the economy a unique, stable path and to keep inflation expectations anchored.

Commitment versus Discretion: The Problem of Promises#

A central bank can operate under two different strategic frameworks. Under discretion, it re‑optimises every period, taking the public’s current expectations as given. Under commitment, it binds itself to a future plan, even if that plan would not be chosen afresh later on.

Why does this matter? In forward‑looking models, today’s inflation depends on what firms expect about future economic conditions. A central bank that can commit to future tight policy, if needed, can influence those expectations today. Under discretion, the bank will be tempted to renege: once private‑sector expectations are set, it may prefer to engineer a little surprise inflation to boost output in the short run. But the public understands this temptation, so expected inflation rises, and the result is an inflation bias—inflation is higher on average with no gain in output. Commitment solves the time‑inconsistency problem by tying the bank’s hands, leading to lower and more stable inflation.

Commitment: A policy strategy in which the central bank pre‑announces a complete future path for its instrument and sticks to it, even if later conditions might tempt it to deviate.

Discretion: A policy approach where the central bank sets its instrument each period afresh, treating the current state as a new optimisation problem without binding itself to past promises.

The intuition is like a parent who promises a child, “If you eat all your vegetables, you’ll get a small dessert.” After the vegetables are eaten, the parent might cheat and give no dessert, knowing the child can’t undo the eating. But the child, foreseeing the cheat, won’t eat the vegetables in the first place. Commitment makes the promise credible.

📝 Section Recap: When the private sector is forward‑looking, a central bank that can commit to future actions can achieve better outcomes than one that acts with discretion, because commitment avoids the inflation bias and improves the trade‑off between inflation and output.

Labour Market Frictions and Sticky Wages#

The previous sections developed the demand side, but the full transmission mechanism depends on how prices and wages are set. Real‑world labour markets are not perfectly flexible. Two important frictions matter.

First, wage stickiness. Many workers’ wages are set in contracts or by norms and adjust only gradually. Even if the central bank cuts the interest rate, boosting demand for goods, firms can only increase production if they can hire more workers without instantly pushing wages up too much. Sticky wages mean that firms’ real marginal costs do not jump wildly, which in turn leads to inflation that moves slowly, as described by the New Keynesian Phillips curve that links today’s inflation to expected future inflation and the output gap.

Second, search and matching frictions. Workers and vacancies do not always find each other instantly. It takes time and effort to match a job seeker with an employer. This search process creates equilibrium unemployment. When demand falls, firms post fewer vacancies, and unemployment rises more than it would in a frictionless market. These frictions shape the natural rate of unemployment and affect how costly output fluctuations are for workers.

Wage stickiness: The tendency of nominal wages to adjust slowly to changes in economic conditions, often due to long‑term contracts, social norms, or menu costs.

Search and matching frictions: The real‑world process by which unemployed workers and open vacancies need time and resources to find each other, giving rise to equilibrium unemployment even in normal times.

Together, sticky wages and search frictions determine the slope of the Phillips curve—how sensitive inflation is to the output gap—and the natural level of output itself. They also affect the welfare losses from booms and recessions, which we quantify next.

📝 Section Recap: Labour market imperfections such as sticky wages and search frictions make the link between demand and inflation gradual, and they determine both the natural level of output and the social cost of output fluctuations.

A Welfare‑Based Loss Function: What Should the Central Bank Care About?#

A central bank doesn’t just chase arbitrary numbers; it acts to improve social welfare. Economists can derive an explicit welfare‑based loss function from the same household utility that gave us the Euler equation. Under standard assumptions—including sticky prices and wages—the average household’s welfare loss from fluctuations can be approximated by a quadratic function (squared gaps) of inflation and the output gap:

Here is the deviation of inflation from target, is the output gap, and is a positive weight that depends on the degree of price and wage stickiness. When both prices and wages are sticky, is smaller than it would be with only sticky prices, meaning the central bank should place relatively more weight on stabilising inflation than the output gap. Search frictions also influence through the cost of unemployment fluctuations.

Welfare‑based loss function: An expression, derived from the preferences of households, that tells us how much society suffers from inflation volatility and output gap volatility, providing a formal objective for monetary policy.

This loss function justifies the idea that a central bank should care about both inflation and the output gap, but with a specific, welfare‑consistent relative weight. It also provides a metric to evaluate different policy rules and targeting regimes.

📝 Section Recap: The central bank’s goal can be distilled into a quadratic loss in inflation and the output gap, with weights derived from household welfare, reflecting the costs of price and wage rigidities.

Intermediate Targets: Nominal GDP and Price‑Level Targeting#

So far we have assumed the central bank targets inflation directly. But other intermediate targets can be useful, especially when the private sector is forward‑looking. Two prominent alternatives are price‑level targeting and nominal GDP targeting.

Under price‑level targeting, the central bank commits to returning the price level to a predetermined path after any deviation. If a temporary shock pushes the price level up, the bank must engineer a period of below‑target inflation to bring the level back down. This creates history‑dependence: a past mistake must be undone. For forward‑looking firms and households, this commitment stabilises long‑run price expectations more strongly than simple inflation targeting, improving the short‑run trade‑off between inflation and output.

Price‑level targeting: A monetary policy regime that aims to keep the consumer price level on a steadily rising path, requiring any past overshoot to be corrected with an equal undershoot.

Nominal GDP targeting goes one step further. Let be the price level and real output. The central bank targets the path of nominal GDP, , or, in logarithms, . If a supply shock reduces real output and raises prices, nominal GDP may not change much, automatically allowing some offset. If aggregate demand falls, both output and prices drop, so the central bank must ease aggressively to hit its nominal GDP target. This regime provides a built‑in stabilisation mechanism that shares risk between inflation and output volatility without needing to estimate the output gap in real time.

Nominal GDP targeting: A regime in which the central bank aims to keep the sum of the log price level and log real output on a pre‑specified growth path, thereby responding to both price and output developments.

These regimes are just different ways to achieve the welfare goal. Price‑level targeting cares more about inflation volatility than standard inflation targeting, while nominal GDP targeting blends the two objectives into a single index. The choice of target influences how firmly expectations are anchored and how well the central bank can handle shocks.

📝 Section Recap: Alternative intermediate targets, such as price‑level or nominal GDP targeting, build history‑dependence into policy, which can anchor expectations more strongly and improve the trade‑off between inflation and output stability.

Summary#

We’ve seen how monetary policy affects aggregate demand, starting from how a household chooses between spending and saving. That choice gives us the forward‑looking IS curve: the output gap depends on the real interest rate and expectations about the future. The central bank uses a rule like the Taylor rule to set interest rates. To keep the economy stable, the bank must follow the Taylor principle and raise real rates when inflation rises. Commitment to a future policy path avoids the inflation bias that comes with discretion. Labour market frictions make inflation adjust slowly and determine how painful booms and recessions are, which is captured in a welfare‑based loss function. Finally, other targeting regimes like price‑level targeting or nominal GDP targeting can anchor expectations even more firmly.