Question 4. This question asks you to derive a money multiplier when there are different types of consumers, who behave differently in terms of how much cash they hold, and different types of banks, which behave differently in terms of how much excess reserves they hold. Suppose that there are two types of consumers; call them type-a consumers and type-1) consumers. Typea consumers hold ca dollars in cash for every dollar they hold in deposits; type-b consumers hold Cb dollars in cash for every dollar they hold in deposits. Let 0,, denote the total amount of cash held by type-a consumers, and let 0;, denote the total amount of cash held by type-b consumers. Let 1),, denote the total amount of deposits held by type-a consumers, and let Db denote the total amount of deposits held by type-b consumers. Let D to denote the total amount of deposits in the economy; let 0 denote the total amount of cash in the economy; let R denote the total amount of reserves in the economy; let ER denote the total amount of excess reserves in the economy; let RR denote the required reserves, let MB denote the monetary base. It remains true that the denitions of the money supply, the monetary base, and total reserves are: M=C+D, MB =C+R, R=RR+ER. Let 7'? denote the required reserve for each dollar deposity and 6 denote the excess reserve ratio for each dollar deposit. Notice that the following identities also apply: C = Ca + Cb EE D = Da + Db. Let a be the fraction of all deposits held by type-a consumers. The money multiplier is still defined as m = M / MB .a Provide an expression for C /D in terms of Ca , Co , and a . b) Using the definition of m , M and MB , find the money multiplier in terms of a , rr , e , Ca and Cb . c) Suppose that Ca > Co and rr te