Question $1($fiscal stimulus$).$ This question is related to lecture $19.$ The government can stimulate the economy via fiscal policies. However, not all policies are equally efficient, and the exact policy to be enacted depends on the purpose. This question tries to discuss some of the nuances. In class, we said that fiscal stimulus can happen in many ways such as direct investment, taxes cuts, etc. For simplicity, in this question, we will only consider the simplest type of policy which is to directly give people money $$ similar to the stimulus checks handed out by the U$.$S$.$ federal government during COVID. The aspect we want to think about is who to give the money to$.$ Suppose the U$.$S$.$ population consists of poor people, middle$-$class people, and rich people. Suppose there are only three kinds of consumption: food, housing, and diamonds. Let$$s introduce a new concept called $$marginal propensity to consume$($MPC$)\mathrm{.}1$ A person$$s MPC is defined as $$how much one spends each additional dollar of income$.$ For instance, if for every dollar of income given to me$,$ I spend $70$ cents, then my MPC is $70\%.($a$)(1$ point$)$ Please compute the MPC for the poor, the middle$-$class, and the rich using the information below.

i$.$ For every dollar given to the poor, they spend $70$ cents on food, $25$ cents on housing, and save the rest.