This question is about the Baumol-Tobin model. For this question, state your ans

Question

This question is about the Baumol-Tobin model. For this question, state your answers in terms of income (Y), money holdings (M), interest (i), Number of trips to the bank (N), and cost of trips to the bank (F) over a single period.

What are average money holdings in the Baumol-Tobin model?

How much interest is foregone by holding money in the Baumol-Tobin model?

What are the costs of visits to the bank in the Baumol-Tobin model?

What is the total cost of money management in the Baumol-Tobin model?

What is the cost minimizing number of trips to the bank?

What are average money holdings?

What happens to money demand if income increases by a factor of 9?

What happens to money demand if the interest rate quadruplues (x4)?

What happens to money demand if the fixed cost of trip to the bank is reduced by 75%?

Assume the price level (P) equals one. Velocity is defined as Y/M. What is velocity in the Baumol-Tobin Model?

What happens to velocity if the fixed cost of trip to the bank is ¼ of its previous value?

In the early 1980s the behavior of M1 and M2 changed dramatically, especially the velocity of M1 and M2 (the ratio of M1 and M2 to the money base). One explanation that was given for this change was the introduction of automatic teller machines which made withdrawing money much more convenient. Given your knowledge of the Baumol-Tobin model, do you think it is reasonable to think that this technological change would affect broader monetary aggregates like M1 and M2?

Explanation / Answer

If

Income: Y,

Average Money Holdings: M,

Interest: i,

Number of withdrawals (Bank trips): N and

Cost of withdrawals (Bank trips): F, then

Total cost of money management, TC = Cost of bank trips (Withdrawals) + Interest foregone by holding cash

= (N x F) + (i x M)

Average money holding, M = (Income / Number of bank trips) / 2

Or, M = Y / 2N

So,

TC = N x F + [i x Y / 2N]

(1) Average money holdings, M = Y / 2N

(2) Interest foregone = i x M

(3) Costs of bank visits = N x F

(4) Total cost of money management, TC = N x F + [i x Y / 2N]

(5) Optimal N can be found by setting [d(TC) / dN] = 0

Or,

F - [i x Y / 2(N2)] = 0

[i x Y / 2(N2) = F

2(N2) = i x Y / F

(N2) = i x Y / 2F

N = [i x Y / 2F]0.5

(6) Average money holdings = Y/(2N)

(7) Demand for Money, M = [FY / (2i)]0.5  [Since M = Y/2N]

If Y1 = 9Y, then

New Money demand, M1 = [F(9Y) / (2i)]0.5 = [FY / (2i)]0.5 x (9)0.5 = M x 3 = 3M

So, money demand trebles.

(8) Now, i1 = 4i

New Money demand, M1 = [FY / (2 x 4i)]0.5 = [FY / (8i)]0.5 = [FY / (2i)]0.5 x (8)-0.5 = M x 0.35

M1 / M = 0.35

(9) If N reduces by 75%, new N (N1) = 0.75N

Since M = Y / (2N),

New demand for money, M1 = Y / 2 x (0.75N) = (Y / 2N) x (1 / 0.75) = M x 1.33

So, M1 / M = 1.33

NOTE: Out of many questions clubbe together, the 1st 9 questions are answered.

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