If government purchases decrease by $10 billion with other factors held constant, calculate the change in the level of real GDP demanded when the MPC is .9.

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Gross domestic product (GDP) describes an economy's total demand. Government spending directly correlates with the direction of GDP demand. When government spending increases, real GDP demand increases, and when government spending decreases, real GDP demand decreases. In this question, government spending on purchases decreases. We consequently know that the change in the level of real GDP (RGDP) will show a correlational decrease. The expenditure multiplier is required because the change in total demand is the result of a decrease in government spending. In contrast, when a change in total demand is because of a change in government taxes, then the tax multiplier is required. The expenditure multiplier is the quotient of 1 divided by (1-MPC).

We know the MPC (marginal propensity to consume) is 0.9, so the expenditure multiplier (also called spending multiplier) is 1/(1-0.9) = 10.0. When the MPC is 0.9 and the expenditure multiplier is 10, decreases in purchases made by the government change the level of real GDP demanded by a factor of 10 times the amount of the spending decrease. In this case, the change in the level of real GDP demanded is a negative $10 billion multiplied by the expenditure multiplier of 10: change in RGDP demanded is the spending decrease of -$10 billion x expenditure multiplier of 10 = RGDP decrease by -$100 billion. Because of the multiplier effect, where a change in spending or taxes equals more than an equal change in GDP, the government's decrease in spending by -$10 billion results in a much greater decrease of -$100 billion in real GDP demanded.

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MPC refers to the marginal propensity to consume, while MPS means marginal propensity to save. In addition, MPC + MPS = 1. These two ratios are used to show what people prefer to do with their money—save or consume. In this case, since the MPC (0.9) is greater than the MPS (0.1), individuals are more likely to spend their money on the purchase of goods and services than to save it. Thus, the overall consumption is likely to increase and contribute to GDP growth.

However, in this question, it is said that only the government expenditure changes, and consumption remains constant. Hence, the overall effect on real GDP will be different. To calculate the actual change, you need to find the multiplier, which is determined by dividing 1 by the MPS—in this case, it is 10.

Since government spending reduces by $10 billion, the real GDP also goes down, by $10 billion * 10 multiplier = $100 billion.

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Real GDP= [1 / (1-MPC)]*X

Where: MPC= Marginal propensity to consume

                X= Decrease in government purchases

Thus,

1/ (1-0.9) =10

=10*10 billion

=$100 billion

Since a reduction in government spending reduces the Real Gross Domestic Product, the government’s reduction of purchases by 10 billion has a resultant effect of lowering the Real Gross Domestic Product by $100 billion.

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In order to determine the change in the level of real Gross Domestic Product demanded, we will have to determine what the expenditure multiplier is and use that multiplier to find the impact of the reduction in government spending.

We know that the formula for finding the spending multiplier is

Multiplier = 1/(1 – MPC). 

Since we have the MPC given in this question, it is easy to find the multiplier.

Multiplier = 1/(1-.9) = 1/.1 = 10.

So, the multiplier in this scenario is 10.  That means that any change in government spending will change the level of real GDP demanded by 10 times the amount of the change.

We can then use the following equation to calculate the change in RGDP demanded. 

Change in RGDP = change in government purchases x multiplier.

Change in RGDP = -$10 billion x 10

Change in RGDP = -$100 billion.

This means that the decrease in government spending ($10 billion) will reduce the amount of RGDP demanded by $100 billion.

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