Macro HW #6

ECON 805 Tracy Deeter

HW #6 3/30/04

1. MPC = 0.80.

a. Marginal Propensity to Save (MPS) = 1 – MPC = 0.20.

f. Intuitively, a change in exogenous spending causes the income of someone else to increase. In turn, they spend a percentage of that increase in income. Now, their spending translates into more income for someone else who likewise spends a percentage of that increase in income. Thus, an initial change in exogenous spending has a much larger affect than simply that initial amount!

g. If the government increases spending by $100, the Keynesian equilibrium level of output will increase as the expenditures line will be shifted up by $100.

ii.

h. If the government increases taxes by $100 via a lump sum tax, equilibrium output will decrease. However, unlike the change in government spending, the change in taxes works indirectly through its affects on disposable income. Thus, the increased taxes will cause consumption to decrease by only a percentage of the tax (since people save and consume their income).

ii.

i. If the government had instituted the spending increase and the tax increase simultaneously, the net effect on equilibrium output would be a positive 100. This situation is often referred to as the balanced budget multiplier. So, in essence the multiplier is one and the initial change in spending / change in taxes is equal to the change in output.

j. A = 1,000,000 and MPC = 0.08

ii.

iii.

Therefore, the tax rate would have to be less than .0025% in order for output to rise after the spending and tax increase.

iv.

Yes, the government could possibly balance the budget. The component that is tricky with regards to balancing the budget is the fact that government tax revenues change automatically over the course of the business cycle. This feature is often referred to as built-in stability. The more progressive the tax system, the greater the economy’s built in stability. Tax revenues T vary directly with GDP, and government spending is assumed to be independent of GDP. So, if we assume our budget is balanced initially and the government increases spending by a certain amount, then the government expenditures line simply shifts up and a deficit occurs. However, as GDP increases, tax revenues will also increase thereby eliminating the deficit and restoring equilibrium.

With regards to our example, if we assume A = 1,000,000 and MPC = 0.08 and our goal of increased government spending was to increase output from 5,000,000 to 5,000,100. We can see that a tax rate of 0.00002 or .002% would result in output increasing to 5,000,100. And, if you take the tax rate of 0.00002 times this new income level of 5,000,100 you will see that tax revenues are 100 which is the amount needed to keep our budget balanced and cover the increased government spending of 100.

Therefore, when income is taxed at a rate of t, the multiplier becomes 1/(1 – c(1 – t)).

a. The Classical and Keynesian theories are very different with regards to the dynamics of saving and investment.

In the Classical model, the interest rate is the reward for delayed consumption. In other words, people are deciding whether to consume now versus to consume later. We discount future consumption. Therefore, if I borrow $1 from you, you will expect me to pay back more than $1 so that you are indifferent/equal between consuming today and consuming tomorrow. This is why the supply of loanable funds (savings) is upward sloping. Likewise, the demand for loanable funds (investment) is downward sloping since firms must pay the interest rate to borrow money. Thus, if the interest rate is high, firms will only invest a little since they will need a high rate of return to cover the interest. It is this interaction of supply and demand of loanable funds (or savings and investment) that determine interest rates. Now, in the Classical model, Savings always equals investment. In addition, since holding cash yields no interest, people only save in bonds. There’s no advantage to holding money or, in other words, you don’t benefit from liquidity! Last of all, money is simply a veil in the Classical model. It is neutral and has no effect on real variables. A change in money supply will simply equate to a change in the price level. The money market simply tells us the price level!

On the other hand, the Keynesian model takes a different stand with regards to saving, investment, and money. As for savings, in the Keynesian model savings depends on income, not the interest rate. As for investment, the Keynesian model recognizes that investment does depend on the interest rate. However, the interest rate is not a huge factor in determining the level of investment, rather expectations on future economic activity play the biggest role in determining the level of investment. This is why investment is extremely volatile and considered the culprit behind business cycles! In addition, the interest rate now represents the reward for reduce liquidity. In other words, when you buy bonds, you are sacrificing the liquidity of cash. The Keynesian model believed that there are three sources of demand for money. One source is transactions demand. This simply means that people demand money in order to buy things. Transactions demand is based highly on income. Another source is precautionary demand. This represents the money you demand/need for unexpected purchases. Once again, precautionary demand depends highly on one’s income. And, the last source of demand for money is speculative demand. Speculative demand revolves around savings and whether or not you save in cash versus bonds, which earn a fixed interest. The interest rate equals the fixed return on the bond divided by the price of the bond. Thus if the interest rate is high, the price of bonds will be low and you will opt to buy more bonds, and therefore demand less money. Likewise, if the interest rate is low, the price of bonds will be high and you will opt to buy fewer bonds, and therefore demand more money. Since the interest rate is now determined in the money market, the role of money is now important. For example, if the money supply increases, interest rates will now fall. When interest rates fall, investment will increase and therefore output will also increase. Thus, unlike in the Classical model, in the Keynesian model money has the ability to affect output!

b. In the Classical model, it is assumed that savings always equals investment. So, if savings falls short of investment (savings < investment), the interest rate will rise. As the interest rate increases, people will be more willing to sacrifice current consumption for future consumption (since the reward for delayed consumption is now higher). Likewise, businesses will be less willing to invest when the interest rate is higher since they will need a higher rate of return to cover the interest. Thus, the interest rate will continue to rise until equilibrium is restored!

c. In the Keynesian model, the relationship between savings and investment isn’t governed by the interest rate. So, if savings falls short of investment, (savings < investment), our inventories are shrinking. What the Keynesian model predicts is that firms will increase output in order to meet the increased expenditures.

If people are optimistic and spending a larger percentage of their incomes, the marginal propensity to consumer has increased. Since the MPC is larger, the slope of the expenditures line is steeper. Due to this change in the expenditures line, expenditures will now be greater than the previous income level. Thus, inventories will be falling. The Keynesian model predicts that output and employment will increase to meet the increased expenditures. It is feasible that output can increase since they assume unemployment exists!

ii.

If people are optimistic and spending a larger percentage on their incomes, the Classical model would argue that savings decreases by the same amount that consumption increased. In addition, since savings = investment, if savings decreases then investment must also decrease. Therefore, the increase in consumption is completely negated by the decrease in investment. Thus, output and employment remain unchanged! This optimistic behavior has only resulted in an increase in interest rates!

If businesses expect favorable economic conditions and increase investment, the expenditures line will shift up by the amount of the change in investment. This will result in a larger increase in output due to the multiplier effect. Expenditures will be greater than the previous income level. Thus, inventories will be falling. The Keynesian model predicts that output and employment will increase to meet the increased expenditures. It is feasible that output can increase since they assume unemployment exists!

ii.

If businesses expect favorable economic conditions and increase investment, the demand for loanable funds must have increased. With the Classical model, since savings = investment, this also means that savings increased by the same amount that investment increased. However, if savings increases, consumption must decrease by the same amount. Thus, consumption decreases by the amount that investment increases. This means that there will be no impact on output or employment!

i. If the money supply increased, interest rates will fall in the Keynesian model. As interest rates fall, investment increases. The increased investment shifts the expenditures line up. Now, expenditures are greater than the previous income level. Thus, inventories will be falling. The Keynesian model predicts that output and employment will increase to meet the increased expenditures. Once again, it is feasible that output can increase since they assume unemployment exists!

ii. If the money supply increased, prices will rise in the Classical model. As prices rise, real

wages temporarily fall. This creates a temporary shortage of labor. However, since wages and prices are perfectly flexible, firms will increase nominal wages to attract workers until the original real wage is restored. Therefore, the overall impact of increasing the money supply is simply an increase in prices and the nominal wage. The real wage, employment, and output remain unchanged!