2. An economy is described by the following equations:

( ) = + − −

= −

=

=

= −

=

=

C Y T r I r G

T L Y r M

Y Desired consumption Desired investment Government purchases Taxes Real money demand Money supply Full-employment output

130 0.5 500 .

100 500 .

100.

100.

0.5 1000 .

1320.

500.

d d

Note that the expected rate of inflation is assumed to equal zero so that money demand depends directly on the real interest rate, which equals the nominal interest rate.

a. Write the equations for the IS and LM curves.

(These equations express the relationship between r and Y when the goods and asset markets, respec tively, are in equilibrium.)

b. Calculate the full-employment values of output, the real interest rate, the price level, consumption, and investment.

c. Suppose that, because of investor optimism about the future marginal product of capital, the invest ment function becomes

= − I r 200 500 . d Assuming that the economy was initially at full employment, what are the new values of output, the real interest rate, the price level, consumption, and investment in the short run? In the long run?

Show your results graphically.