The IS* curve illustrates the relationship between output and the real exchange rate, and represents equilibrium in the goods market. A reduction in the real exchange rate will boost net exports and therefore increase output.
The LM* curve represents equilibrium in the money market. Money demand and money supply are not affected by changes in the real exchange rate so therefore the LM* curve is vertical.
The increase in government spending will increase output and put upward pressure on the interest rate. The interest rate will be inclined to rise due to the reduction in national saving and the increase in money demand. To keep the interest rate fixed at the world rate there will be capital inflow and this will increase demand for the currency. The real exchange rate will rise.
The increase in income taxes will shift the IS* curve to the left. This will reduce spending and output in the economy. Interest rates will tend to fall and this will cause an outflow of funds. The real exchange rate will fall. To keep the real exchange rate fixed the money supply will have to fall to push the interest rate back to the world level and prevent the outflow of funds.