At present the currency with the people and their demand deposits with banks contribute $200$ million to the economy. This value is derived from the people$’$s behavior where they used to deposit $80\%$ of their money and$\mathrm{ 2}0\%$ take it as cash. Also, the banks have to maintain the required reserve of $10\%.$

i$.$ Calculate the size of high$-$powered money.

ii$.$ How does the answer $($i$)$ change for bank reserves ratio of a$)$ zero percent; b$)5$ percent; and c$)20$ percent?

iii. How does the answer $($i$)$ change for general public cash holding of a$)$ zero percent; b$)5$ percent; and c$)100$ percent?