Use the dynamic macroeconomic model to analyse the likely effects on the real interest rate of the following scenarios. Explain the changes that happen using a graph by showing which curve shifts towards which direction. Do not forget to include wealth effects when necessary.

1. An anticipated slowdown in the pace of technological discoveries (interpret this as the expected level of future TFP being lower than previously thought.)
2. The life expectancy increases but there is no increase in the age of retirement. [Hint : You can elaborate on how it is more difficult for older people to work, so they will supply more labour while they can to save for retirement. The higher marginal rate of substitution between future leisure and consumption leads to a lower future employment.]
3. Climate change that brings greater risks of natural disasters that destroy some of the economy's capital stock.