Suppose that the price level is fixed in the short run so that the economy doesn't reach general equilibrium immediately after a change in the economy. For each of the following changes, what are the short-run effects on the real interest rate and output? Assume that, when the economy is in disequilibrium, only the labor market is out of equilibrium; assume also that for a short period firms are willing to produce enough output to meet the aggregate demand for output.

1. a decrease in the expected rate of inflation.

2. an increase in consumer optimism that increases desired consumption at each level of income and the real interest rate.

3. a temporary increase in government purchases.

4. an increase in lump-sum taxes, with no change in government purchases(con-sider both the case in which Ricardian equivalence holds and the case in which it doesn't) For this question, please state ricardian equivalence first.

5. a scientific breakthrough that increases the expected future MPK.