How to do the question. Please write steps for all parts.

Q4. Consider an interaction between a dictator and an investor. The investor first chooses to invest or not. Investment costs 20 dollars up front each period and produces revenue of 100 dollars at the end of each period. Hence investment yields a profit of 80 in a given period. If the investor chooses not to invest she gets nothing. If the investment is made, the dictator chooses whether to tax or steal. That is, he can steal the entire revenue of the firm or tax the profits of the firm at rate t, where 0