University of Texas ECO 34730_Solutions to IS-LM Practice Problems

Solutions to IS-LM Practice Problems 1) Reproduce the following comparative static results: Effect of an increase in on Y r C I G + + ? - CS + + + - SP + + ? + T - - - + M + - + + P - + - - M T + - + + a) Increase in G: see IS-LM notes. b) Increase in CS: An increase in CS shifts the IS curve to the right. Thus, interest rates (r) and income (Y) must rise. For investment, since animal spirits are unchanged, only the interest rate matters. Thus, since r goes up, I must fall. For consumption, the effect looks ambiguous when using the consumption function (Y up means C up, r up means C down, CS up means C up), but in fact we can state that consumption must, in fact, go up. The key is to recall the National Income Accounting Identity = + + Note that G is unchanged. We know Y must go up and I goes down. But if the Left-Hand Side of the equation goes up, the Right-Hand side must rise as well. Since I is falling and G is unchanged, the only way for C+I+G to go up is if C went up. c) Increase in SP: An increase in Animal Spirits shifts the IS curve right, so the interest rate and income must rise. The response of investment is tricky. It appears ambiguous, based on the investment function (SP up means I up, r up means I down), but in fact we can show that Investment had to go up. To see this consider the loanable funds diagram. The increase in SP means the investment demand curve shifts right. Then, the fact that Y goes up (from IS-LM outcome) means the savings curve must also shift right. However, the latter shift cannot be too big since we know that, in the end, the interest rate must end up higher than at the start. In any case, the rightward-shift in investment demand and the rightward-shift in the supply of savings function both increase investment. Thus, investment goes up even though the interest rate rises. For consumption, the consumption function implies an ambiguous change in consumption since the income and interest rate effects are pushing consumption in opposite directions. d) Increase in T: An increase in taxes shifts the IS curve left, thereby lowering interest rates and output. The decrease in interest rates means investment must go up (since SP is unchanged). Finally, since G is unchanged and I must rise, only a decrease in consumption can account for the decrease in GDP based on the national income accounting identity. e) Increase in M: An increase in the money supply shifts the LM curve right, lowering interest rates and raising GDP. Investment must rise since interest rates fell and SP is unchanged. Consumption must rise since income went up, interest rates fell, and taxes and consumer sentiment are unchanged. f) Increase in P: An increase in prices is equivalent to a decrease in the real money supply, thus shifting the LM curve left. Answers are same as for increase in M but signs are reversed. g) Increase in MT: An increase in MT shifts the LM curve right, so the results are the same as for an increase in money supply