Suppose an economy where 2,000 young agents are born in every period t. Each young individual is endowed with 80 units of the consumption good. The young do not hold any fiat money; instead, they hold deposits to finance consumption later in life. In fact, each young individual deposits 50 units of the consumption good with banks. They do not invest in capital. Deposits at banks are subject to a reserve requirement of 15 percent. After meeting the reserve requirement, banks invest the remainder of all deposits into capital. The net real rate of return on capital is 3 percent per period. The monetary base controlled by the Central Bank is constant and equal to 5,000 units of fiat money. There is no central bank lending.

(a) Find the equation describing the money market clearing, that is, the equality of total supply and demand for fiat money. Use it to calculate the exact price level in units of fiat money.

(b) Calculate the total nominal money stock (M1)t . How large is the money multiplier?

(c) (5 points) How large is total output (GDPt) in this economy, assuming that capital needs two periods to produce output and then fully disintegrates? (Hint: There is no unintermediated capital in this economy.)

please answer all 3 questions and show the steps, this is a complete question