Imports as a Leakage from Domestic Expenditure

Imports and Domestic Expenditure

When income rises, households and firms may buy more goods and services from abroad. That spending is an import, and it does not create demand for domestically produced output. In an expenditure model, imports therefore reduce the portion of total spending that supports domestic production. The key measure is the marginal propensity to import: the share of an additional unit of income that is spent on imports.

This is a statement about expenditure, not a claim that imported goods are economically useless or that the money disappears. The payment goes to a foreign producer. The issue for domestic output is that the purchase does not directly generate income for domestic producers. The treatment here is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.

Definition: Imports, denoted $M$, are goods and services produced abroad and purchased by domestic residents. The marginal propensity to import, denoted $m$, is the change in imports divided by the corresponding change in income, when the relationship is linear: $m=\Delta M/\Delta Y$. It measures how much import spending changes when income changes by one unit.

A simple import schedule is $M=M_0+mY$, where $M_0$ is autonomous imports, $Y$ is income or output, and $m$ is the marginal propensity to import. In this model, $M_0$ represents imports that do not vary with current income, while $mY$ represents the income-dependent part. The model assumes a constant $m$ over the range being studied. It is a simplifying expenditure-model assumption, not a claim that imports always respond linearly to income in real economies.

When imports are included in an expenditure schedule for domestic output, they are subtracted from spending on domestic production. For example, if planned consumption includes purchases of both domestic and imported goods, subtracting imports isolates the part of total expenditure that is directed toward domestic output. The earlier material on the consumption function distinguishes consumption from saving; imports are a separate distinction about where purchased output was produced.

Why Income-Dependent Imports Reduce Domestic Demand

Suppose income rises by $\Delta Y$, and the import schedule is linear with constant $m$. The change in imports is $m\Delta Y$. Because that part of the additional spending is on foreign output, it does not add to demand for domestic output. This gives the basic leakage calculation:

\Delta M = m\Delta Y

The relationship follows directly by comparing imports before and after the income change. At income $Y$, imports are $M_0+mY$. At income $Y+\Delta Y$, imports are $M_0+m(Y+\Delta Y)$. Subtracting the first amount from the second cancels $M_0$ and $mY$, leaving $m\Delta Y$. Autonomous imports affect the level of imports, but not the change generated by an income increase in this model.

\begin{aligned} M(Y+\Delta Y)-M(Y) &=[M_0+m(Y+\Delta Y)]-[M_0+mY]\\ &=m\Delta Y \end{aligned}

In successive spending rounds, some income is spent on consumption, and part of that consumption may be imported. The imported component is subtracted when identifying the round's contribution to domestic demand. In the simple model where consumption changes by $c\Delta Y$ for a change in income, and imports change by $m\Delta Y$, the induced change in domestic demand for that round is $c\Delta Y-m\Delta Y$. This calculation describes one round; it does not by itself sum all rounds into a total multiplier.

The import leakage is additional to saving as a leakage from the expenditure stream. Saving is income not spent on current consumption; imports are spending directed to foreign-produced goods and services. They represent different reasons that a rise in income may fail to create an equivalent rise in demand for domestic output.

Worked Applications

Worked Example: Finding the Marginal Propensity to Import

A hypothetical island economy is represented by the import schedule $M=20+0.12Y$, with income and imports measured in thousands of dollars per year. Find imports at income of $1,000 thousand and $1,250 thousand, and calculate the import change and marginal propensity to import.

Method. Substitute each income into the schedule, then divide the change in imports by the change in income. The model assumes the stated linear schedule applies at both income levels.

At $Y=1{,}000$, income-dependent imports are $0.12(1{,}000)=120$. Adding autonomous imports gives $M=20+120=140$ thousand dollars.

At $Y=1{,}250$, income-dependent imports are $0.12(1{,}250)=150$. Total imports are $M=20+150=170$ thousand dollars.

Income increases by $1{,}250-1{,}000=250$ thousand dollars. Imports increase by $170-140=30$ thousand dollars. Therefore, $m=30/250=0.12$, or 12 cents of additional imports per additional dollar of income.

Check. The schedule predicts an import increase of $0.12(250)=30$ thousand dollars, matching the direct difference. The autonomous amount of 20 thousand dollars cancels from the change.

Worked Example: Tracking Imports Through Spending Rounds

A domestic purchase creates an initial $600 increase in income. Assume no taxes, a marginal propensity to consume $c=0.70$, and a marginal propensity to import $m=0.10$. For the first three induced rounds, calculate induced consumption, the import component, and the induced demand for domestic output. Treat these as changes from the initial equilibrium; assume the propensities stay constant.

Method. For each round, multiply the income created in that round by $c$ to find induced consumption and by $m$ to find induced imports. Subtract induced imports from induced consumption to identify the round's induced demand for domestic output. The common mistake of applying $m$ to consumption rather than income is avoided by using the round's income at each step.

The initial purchase creates $600 of income. For the first induced round, consumption is $0.70(600)=\$420$, and imports are $0.10(600)=\$60$. Thus the induced domestic demand is $\$420-\$60=\$360$.

That $360 of domestic demand is the income change associated with the next round. Induced consumption is $0.70(360)=\$252$, imports are $0.10(360)=\$36$, and induced domestic demand is $\$252-\$36=\$216$.

For the third round, the income change is $216. Induced consumption is $0.70(216)=\$151.20$, imports are $0.10(216)=\$21.60$, and induced domestic demand is $\$151.20-\$21.60=\$129.60$.

Check. In each round, domestic demand is 60% of that round's income change, since $0.70-0.10=0.60$: $0.60(600)=360$, $0.60(360)=216$, and $0.60(216)=129.60$. The rounds get smaller because the induced domestic demand is less than the income change that started each round. This example traces only the stated rounds.

Worked Example: Marginal and Average Import Shares

A hypothetical economy has imports $M=25+0.09Y$, where values are in thousands of dollars per year. At income of $1,200 thousand, calculate total imports and the average import share $M/Y$. Then calculate the import increase if income rises by $200 thousand, and distinguish the marginal propensity to import from the average share.

Method. Use the full schedule to find the import level and the coefficient $m$ to find the response to an income change. The average share uses total imports divided by total income; it is not the same calculation as the marginal propensity.

At $Y=1{,}200$, the income-dependent part is $0.09(1{,}200)=108$ thousand dollars. Total imports are $25+108=133$ thousand dollars. The average import share is $133/1{,}200=0.110833\ldots$, or approximately 11.08%.

If income rises by $200 thousand, the import increase is $0.09(200)=18$ thousand dollars. Equivalently, the schedule gives imports of $25+0.09(1{,}400)=151$ thousand dollars at the new income, and $151-133=18$ thousand dollars more than before.

The marginal propensity to import is 0.09, or 9%, while the average import share at the original income is approximately 11.08%. They differ because total imports include the autonomous amount of $25 thousand, whereas the marginal propensity measures only the change associated with a change in income.

Check. At the higher income, the average import share is $151/1{,}400$, approximately 10.79%. It has fallen even though the marginal propensity remains 9%, because the fixed autonomous amount is a smaller share of the higher income.

Common Mistakes and Interpretation

A frequent error is to treat the marginal propensity to import as a share of consumption rather than a share of income. In the second example, the incorrect calculation would be $0.10(420)=\$42$, applying the import propensity to the $420 of induced consumption. But the stated model defines imports as a function of income, so the correct first-round import change is $0.10(600)=\$60$. The $420 is the consumption change; the $60 is the import change tied to the $600 income change.

Another trap is to confuse an import level with an import change. If $M=M_0+mY$, total imports include both $M_0$ and $mY$. When income changes, the autonomous amount is unchanged, so only $m\Delta Y$ is induced by the income change. Similarly, $M/Y$ is an average share at a particular income, not the marginal propensity to import.

The simple schedule has limits. The marginal propensity $m$ is assumed constant, and the examples hold other influences on imports fixed. Changes in exchange rates, relative prices, tastes, or trade restrictions could change imports for reasons not captured by an income-only schedule. Do not attribute every observed import change to income unless the model says other determinants are held constant.

Key takeaway: In a linear import schedule $M=M_0+mY$, $m$ measures the import increase per additional unit of income. Since imported goods are not domestic output, the induced import component must be excluded when measuring how much a spending round adds to domestic demand.

Check Your Understanding

For each problem, use the stated simple expenditure assumptions and show the income change to which the import propensity applies.

An economy has $M=18+0.06Y$, with values in thousands of dollars. Income rises from $800 thousand to $1,100 thousand. Find imports at both incomes and the import increase. (Answer: Imports rise from $66 thousand to $84 thousand, an increase of $18 thousand; $m=0.06$, or 6%.)
Income increases by $400, with $c=0.80$ and $m=0.15$. Assuming no taxes, find the induced consumption, induced imports, and induced domestic demand in the first round. (Answer: Consumption $320; imports $60; domestic demand $260.)
Imports follow $M=25+0.09Y$. At $Y=1{,}200$, find total imports and the average import share, then find the import increase for a $200 income rise. Values are in thousands of dollars. (Answer: Imports $133 thousand; average share approximately 11.08%; import increase $18 thousand.)
A $1,000 initial income change occurs with $c=0.65$ and $m=0.05$, with no taxes and constant propensities. Find induced domestic demand in the first round and the next round. (Answer: First round: consumption $650, imports $50, domestic demand $600. Next round: consumption $390, imports $30, domestic demand $360.)
At income of $900 thousand, a linear import schedule gives imports of $102 thousand. The marginal propensity to import is 0.08 and autonomous imports are constant. Find autonomous imports and imports at income of $1,100 thousand. (Answer: Autonomous imports are $30 thousand; imports at $1,100 thousand are $118 thousand.)

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