Spending Feedback and Demand-Shock Amplification

Why Spending Can Have More Than One Effect

An initial change in spending affects more than the transaction that occurs first. When a business sells additional output, the revenue becomes income for workers and other suppliers. Households then use part of their additional disposable income to consume. That consumption creates further demand and, when firms respond with additional production, another increment of income. The process can repeat over several rounds.

This feedback helps explain why a demand shock can produce a larger cumulative change in output than the initial spending change alone. It does not mean that every dollar is spent again: some income is saved, used to pay taxes, or spent on imported goods. The size of the feedback therefore depends on how much of each round of income becomes demand for domestic output.

For the basic round-by-round model, assume prices are fixed, firms can respond to additional demand with additional production, and each dollar of the initial spending change becomes domestic output and income. Assume also that the induced consumption is domestic, that there are no taxes on the additional income, and that no other spending changes occur. These simplifying assumptions isolate the household spending feedback; they are not a complete description of an economy.

Let \(\Delta Y_0\) be the output and income associated with the initial spending change. Let \(\Delta Y_1\) be the next round’s output effect, generated by households’ consumption out of the income from round 0. The later rounds are defined in the same way. A positive shock produces positive round effects under these assumptions; a negative shock produces negative effects.

How the Rounds Follow One Another

The key calculation is recursive: each round’s induced consumption depends on the income change from the round immediately before it. If all the induced consumption is domestic and the whole income increment is disposable, then the next round’s output equals \(c\) times the preceding round’s output.

This relation is a round-by-round accounting rule, not a claim that the change in output occurs all at once. Round 0 is the initial change. Round 1 follows as households spend part of the income generated in round 0; round 2 follows from income generated in round 1. Keeping the timing explicit prevents a common error: counting the initial spending and the later rounds as though they were all the same transaction.

The recursion follows from the definition of \(c\). If round \(t\) creates an income change of \(\Delta Y_t\), then, under the stated assumptions, disposable income changes by that same amount. Households consume \(c\Delta Y_t\). If firms meet that additional domestic consumption demand with additional output, round \(t+1\) output is \(c\Delta Y_t\). When \(0 \leq c < 1\), each successive round has a smaller absolute value than the preceding round, so feedback diminishes. This argument explains the sequence of rounds; it does not require treating the entire sequence as one immediate output response.

Negative Shocks and Cumulative Changes

The same round-by-round logic applies when the initial change is negative. A decline in spending reduces output and income in round 0. Households then reduce consumption in response to lower income, creating a further negative effect. Multiplication by a positive \(c\) preserves the negative sign; it does not turn a contraction into an expansion.

When Some Consumption Does Not Become Domestic Output

The basic recursion assumes all induced consumption creates demand for domestic output. If some of that consumption is spent on imports, only the domestic portion contributes to the next round of domestic output. To make that adjustment, let \(r\) be the share of induced household consumption spent on domestic goods and services. Under the same fixed-price and capacity assumptions, the next domestic output effect is \(r\) times household consumption. Since household consumption is \(c\) times the preceding income effect, the round-by-round rule becomes:

Here \(r\) is a domestic-spending share between 0 and 1. The factor \(rc\) is smaller than or equal to \(c\), so this leakage reduces the domestic feedback. Be careful about what each number describes: \(c\) is the share of additional disposable income spent on consumption, while \(r\) is the share of that consumption spent domestically. If the problem gives a percentage spent on imports, the domestic share is one minus the import share.

Common Exam Traps and Why the Feedback Matters

A frequent error is to multiply every round by the initial shock rather than by the preceding round. For example, with an initial $100 million increase and \(c=0.70\), the correct first induced round is \(0.70 \times \$100\) million, or $70 million. The next round is \(0.70 \times \$70\) million, or $49 million. It is not another $70 million: the second round is based on the $70 million income change from round 1.

Another trap is confusing the cumulative change with one round’s change. If a question requests the output effect in round 3, report that round alone. If it requests the total through round 3, include rounds 0, 1, 2, and 3. Also check the sign and units: a negative initial shock produces negative induced rounds in this model, and figures stated in millions should not silently be treated as dollars.

The feedback is useful for interpreting cyclical demand changes because it explains why an initial reduction or increase in spending may be followed by further changes in output. The size and duration of those rounds depend on assumptions about household behavior and how much spending becomes domestic demand. The calculation is therefore a structured short-run illustration, not a universal forecast: changes in prices, capacity, taxes, imports, or other spending can alter the transmission.