Suppose economists observe that an increase in government spending of \(\$ 10\) billion raises the total demand for goods and services by \(\$ 30\) billion. a. If these economists ignore the possibility of crowding out, what would they estimate the marginal propensity to consume \((M P C)\) to be? b. Now suppose the economists allow for crowding out. Would their new estimate of the \(M P C\) be larger or smaller than their initial one?

The multiplier effect is a key economic concept which explains how an initial change in spending leads to a larger change in national income. In the context of the exercise, an increase of \(10 billion in government spending resulted in a \)30 billion boost to the total demand. This illustrates the multiplier in action, where the multiple is three. Such amplification occurs because one person's spending becomes another person's income, thus when the government spends more, it increases the income of the public, who then spend more in turn.

To clarify this concept, think of the government's initial spending as a spark that sets off a chain reaction of expenditures. Each round of spending travels through the economy, causing waves of consumption based on the marginal propensity to consume (MPC), which is the fraction of additional income that a household consumes rather than saves. Mathematically, the size of the multiplier effect is represented by the formula \frac{1}{1-MPC}. It's crucial to note that, in reality, several factors, such as taxes, imports, and price levels, can affect the actual multiplier effect observed in the economy.

Government spending can take many forms, such as infrastructure investment, education funding, or defense budgets. It plays a significant role in a country's economy by influencing employment, resource allocation, and the overall level of demand for goods and services. In the given exercise, an increase in government spending was intended to stimulate the economy by increasing demand.

When the government injects money into the economy, it can lead to increased business activities and higher employment rates as companies respond to growing demand. However, the effectiveness of government spending in stimulating economic growth depends on various factors, including the current state of the economy, levels of existing government debt, and how households and firms adjust their saving and investment behaviors in response to government actions.

The crowding-out effect is a potential downside of increased government spending. It occurs when higher government spending leads to a reduction in private sector investment and consumption. Essentially, when the government borrows money to fund its expenditures, it can lead to higher interest rates. These increased rates make it costlier for businesses and individuals to borrow, which can discourage investment and consumption, offsetting the initial intention of economic stimulation.

In the exercise scenario, accounting for crowding out would reduce the estimated multiplier effect. Since part of the government's spending potentially substitutes the private sector spending rather than adding to it, the actual increase in total demand would be less than expected, leading to a downward revision of the marginal propensity to consume. This is why the new estimate of the MPC, considering crowding out, would be smaller compared to the initial estimate, which ignored the crowding-out effect.