Question

5. Suppose that instead of following the interest rate rule r=r(Y), the central bank keeps the money supply constant. That is, suppose M = M. In addition, suppose that prices are completely rigid, so that the nominal and the real interest rate are necessarily equal; money-market equilibrium is therefore given by M/= = L(r,Y). a. Suppose that the money market is in equilibrium when r = ro and Yo. Now suppose Y rises to Y). For the money market to remain in equilibrium at the initial values of M and P, does r have to rise, fall, or stay the same? b. Suppose we want to show, in the same diagram as the IS curve, the combinations of r and Y that cause the money market to be in equilibrium at a given M and P. In light of your answer to part (a), is this curve upward-sloping, downward-sloping, or horizontal? c. Using your answer to part (b), describe how each of the following developments affects the interest rate and output when the central bank is setting M = M and prices are completely rigid: i. Government purchases rise. ii. The central bank reduces the money supply, M. iii. The demand for money increases. That is, consumers' preferences change so that at a given level of i and Y they want to hold more real balances than before.

Answer 1

The rise in income from YO to Y1 increases demand for money at every rate of interest. To keep the money market in equilibrium given the money supply, an increase in money demand increases the rate of interest. b) From the discussion in (a) it is evident that the curve given M and P depict a positive relationship between Y and r. That is if output increases the rate of interest also rises. Hence, the curve will be upward sloping. c) i ii. As govemment purchase rises, the equilibrium output rises. This increases the rate of interest and the economy move along the curve. An increase in money supply decreases the rate of interest given the money demand. Then for every output level the rate of interest falls due to rise in money supply. Hence, the curve shift to the right due to rise in money supply. The rise in demand for money increases rate of interest at each level of output. The increase in interest at each level of output shifts this cuive to the left. iii.