Circular flow of income: two-sector model

For the basic two-sector model, the investment multiplier is k = 1/(1 − MPC), assuming no government or foreign-sector leakages. With MPC = 0.6, the marginal propensity to save is 1 − 0.6 = 0.4. Therefore, k = 1/0.4 = 2.5. Option D is only the MPS, not the multiplier, so option C is correct.

In the two-sector model, the investment multiplier is k = 1/(1 − MPC). With MPC = 0.75, k = 1/0.25 = 4. The resulting change in income is ΔY = k × ΔI = 4 × 24 = 96. This is the total potential increase after successive rounds of consumption and income generation. Therefore, option B is correct.

When unplanned inventories rise, firms are producing more goods than buyers are planning to purchase. The unsold portion is added to inventories, so planned aggregate expenditure is less than current output. If planned expenditure were greater than output, inventories would fall because sales would exceed current production. Equality between planned expenditure and output would imply no unplanned inventory change.

Falling unplanned inventories mean that buyers are purchasing more than firms are currently producing. Firms meet the excess demand by selling part of their existing stock, so inventories decline. Therefore, planned aggregate expenditure is greater than current output. When expenditure is below output, inventories rise; when the two are equal, there is no unplanned change in inventories.

In the two-sector model, saving represents leakage and investment represents injection. Since investment is 40 while saving is only 25, injection exceeds leakage by 15. This imbalance creates expansionary pressure on planned expenditure, output, and income until adjustment occurs. Equilibrium would require S = I, so option C is not correct, and nothing in the data implies zero consumption.

In the two-sector model, MPC + MPS = 1. Therefore, MPC = 1 − 0.2 = 0.8. The simple investment multiplier is k = 1/(1 − MPC), which is also 1/MPS. Thus k = 1/0.2 = 5. The correct pair is 0.8 and 5. Option C has the correct MPC but an incorrect multiplier, while options A and D incorrectly treat MPS as MPC.

The investment multiplier is k = 1/MPS in a simple two-sector model. With MPS = 0.5, k = 1/0.5 = 2. The total change in income is therefore ΔY = k × ΔI = 2 × 30 = 60. The amount 30 represents only the initial investment increase; the multiplier process generates additional rounds of consumption and income, making 60 the correct total change.

In a closed two-sector economy, households divide income between consumption and saving, so Y = C + S. Planned expenditure consists of consumption and investment, so equilibrium output also satisfies Y = C + I. Equating these two expressions gives C + S = C + I and therefore S = I. This is the saving-investment condition for equilibrium; the other equalities are not generally required.

Household saving is a leakage because it represents income that is not immediately spent on firms’ goods and services. Investment is an injection. If saving rises while planned investment remains unchanged, leakages become greater than injections, consumption demand falls, and firms initially face unsold output. The unsold goods accumulate as unplanned inventories. This disequilibrium continues until output, income, saving, or investment adjusts; equilibrium in the simple two-sector model requires planned saving to equal planned investment.

For a closed two-sector economy without government, equilibrium income is determined by aggregate expenditure: Y = C + I. Rearranging gives I = Y − C. Substituting the values, I = 500 − 420 = 80. Therefore, private investment is 80 units. The figure 420 is consumption and 500 is total equilibrium income; adding them to obtain 920 would violate the equilibrium identity.

Autonomous investment is an initial component of aggregate expenditure that does not depend on current income. When it falls, firms receive less demand and reduce production and income. The lower income then reduces consumption according to the marginal propensity to consume, causing further reductions in other producers’ income. Through these successive rounds, the total decline in equilibrium income is larger than the initial investment decline. This is the reverse operation of the positive investment multiplier.

In the simple two-sector model, the change in equilibrium income is given by ΔY = k × ΔI, where k is the investment multiplier and ΔI is the change in autonomous investment. The multiplier is k = 1/(1 − MPC), so a constant MPC means the multiplier remains fixed. If investment doubles, the size of the income effect depends on the multiplier and the actual change in investment, not on taxes, imports, or an irrelevant product characteristic.

The investment multiplier in the simple two-sector model is k = 1/(1 − MPC), or equivalently k = 1/MPS. When MPC approaches 1, MPS approaches zero. Each successive recipient spends almost all additional income, so the initial investment circulates through many rounds of consumption and income creation. Consequently, the multiplier becomes very large, although it is finite for any MPC strictly below 1. It is close to 1 when MPC is close to zero.

The simple investment multiplier is k = 1/(1 − MPC). When MPC = 0, households do not spend any part of an additional income on consumption, so there are no secondary rounds of expenditure. Substitution gives k = 1/(1 − 0) = 1. Therefore, a rise in investment increases equilibrium income by exactly the initial investment amount; it does not create an additional multiplied increase. The other numerical values do not follow from the multiplier formula.

The real flow consists of physical factor services and physical goods or services. Households supply labour, land, capital and entrepreneurial services to firms, while firms supply the produced goods and services purchased by households. Wages, consumption expenditure, savings and dividends are monetary flows, not real flows. Therefore option A is correct.

In the two-sector model, household saving is a leakage because it is not spent on current consumption. Firms’ investment is an injection because it adds expenditure to the circular flow. The financial market transfers household savings to firms as loans, thereby connecting the leakage of saving with the injection of investment. Hence option A is correct.

When total expenditure exceeds current output, buyers demand more goods than firms have produced during the period. Firms meet part of this excess demand by selling goods from existing inventories. Consequently, inventories decline unexpectedly, creating an unplanned decrease in stock. Thus option B is correct; an inventory increase would occur when output exceeds expenditure.

If expenditure is below output, firms cannot sell all the goods they have produced. The unsold goods accumulate as unplanned inventories, signalling that production is too high relative to demand. To reduce this accumulation, firms are likely to lower output in the next period. Therefore option A is correct. Increasing output would intensify the excess-stock problem.

Firms normally produce on the basis of expected sales. When actual sales turn out to be lower, a portion of the produced output remains unsold. That unsold output is added to inventories without being planned, so unplanned inventories rise. This may later encourage firms to reduce production. Hence option A is correct.

When actual sales exceed expected sales, firms sell more than they had planned. Existing inventories therefore fall unexpectedly, indicating that demand is stronger than anticipated. To replenish stocks and respond to the higher demand, firms are likely to increase production in the next period. Thus option B is correct, although the precise adjustment depends on firms’ expectations and capacity.

Household saving is the part of income that is not used for current consumption. Because it reduces consumption expenditure flowing from households to firms, it temporarily withdraws purchasing power from the circular flow and is called a leakage. Investment is the corresponding injection when savings are channelled back to firms. Therefore option A is correct.

The governing identity is MPC + MPS = 1. The slope of the consumption function is MPC, while the slope of the saving function is MPS. If MPC rises, MPS must decrease by the same amount so that their sum remains one; for example, a rise from 0.70 to 0.80 changes MPS from 0.30 to 0.20. Hence option B is correct. The fall need not make MPS negative.

Household saving is the part of income that is not spent on currently produced goods and services. Consequently, it withdraws purchasing power from the immediate consumption-expenditure stream flowing to firms and is called a leakage. In a simple two-sector model, investment is the corresponding injection that may offset saving.

When consumption exceeds current income, household saving is negative because households are spending more than they earn during the period. They can finance this excess spending by drawing down savings accumulated earlier or by borrowing. Government taxes, exports and stopping factor services do not directly provide the required household purchasing power in this two-sector setting.

In a two-sector economy, equilibrium requires planned saving to equal planned investment, so S = I. National income is initially expressed as Y = C + I, where income is allocated to consumption and investment expenditure. Substituting S for I because S = I gives Y = C + S. Thus, income is also equal to consumption plus saving, making option A correct.