Eco Solutions

Chapter 10

Solutions to the Problems in the Textbook

Technical Problems

1.a. Each point on the IS-curve represents an equilibrium in the expenditure sector. (Note that this is a closed economy, that is, NX = 0).

The IS-curve can be derived by setting actual income equal to intended spending, or

Y = C + I + G = (0.8)[1 - (0.25)]Y + 900 - 50i + 800 = 1,700 + (0.6)Y - 50i ==>

(0.4)Y = 1,700 - 50i ==> Y = (2.5)(1,700 - 50i) ==> Y = 4,250 - 125i.

1.b. The IS-curve shows all combinations of the interest rate and output level such that the expenditure sector (the goods market) is in equilibrium, that is, actual output equals intended spending. A decrease in the interest rate stimulates investment spending, making intended spending greater than actual output. The resulting unintended inventory decrease leads firms to increase their production until actual output is again equal to intended spending. This means that the IS-curve is downward sloping.

1.c. Each point on the LM-curve represents an equilibrium in the money sector. Therefore the LM-curve can be derived by setting real money supply equal to real money demand, that is,

M/P = L ==> 500 = (0.25)Y - 62.5i ==> Y = 4(500 + 62.5i) ==> Y = 2,000 + 250i.

1.d. The LM-curve shows all combinations of the interest rate and level of output such that the money sector is in equilibrium, that is, the demand for real money balances is equal to the supply of real money balances. An increase in income will increase the demand for real money balances. Given a fixed real money supply, this will lead to an increase in interest rates, which will then reduce the quantity of real money balances demanded until the money market clears again. In other words, the LM-curve is upward sloping.

1.e. The level of income (Y) and the interest rate (i) at the equilibrium are determined by the intersection of the IS-curve with the LM-curve. At this point, the expenditure sector and...