Suppose that the money demand function takes the form If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow

Complete Question

Suppose that the money demand function takes the form

(M/P)^d = L(i,Y) = Y/(5i)

a. If output grows at rate and the nominal interest rate is constant, at what rate will the demand for real balances grow

b. What is the velocity of money in this economy

a. See explanation below

b. Velocity = 5i

Step-by-step explanation:

a. Suppose that the nominal interest rate remains constant, the demand for real balances will grow at the same rate at which the output grows.

b.

Given that (M/P)^d = L(i,Y) = Y/(5i)

Money equation is written as;

Total Spending = MV

Where M = Amount of Money..

V = Velocity of Circulation

Total Spending = PY;

So, PY = MV --- Make V the subject of formula

PY/M = V --- Rearrange

V = PY/M (1)

Also,

M/P = Y/5i --- Cross Multiply

M * 5i = P * Y --- Make 5i the subject of formula

5i = PY/M (2)

Compare 1 and 2

5i = V = PY/M

So, 5i = V

V = 5i

Hence, Velocity = 5i

true? is that what you're asking or do you mean something else?

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺