Problem 1 - The inflation tax (35 points) Consider the following information abo

Question

Problem 1 - The inflation tax (35 points)

Consider the following information about the price level P in the years 2014 and 2015 and the money supply M in 2015 for four hypothetical countries

P_2014

P_2015

M_2015

Developed Land

100

101

251,288

Seventies Land

100

110

271,304

Bolivarian Republic

100

200

450,080

Weimar Republic

100

1100

99,440

Assume moreover that the real interest rate r and real GDP in 2015 are the same in all four countries, and given respectively by Y = 50,000 and r = 0.04 (i.e. 4 percent). The money demand function is also common for all four countries and given by

where the nominal interest rate i is the sum of the real interest rate r and the inflation rate ?  .The asset market is in equilibrium when L(Y , i) = M / P. Finally, revenue from the inflation tax is given by

Inflation _ tax _ revenue = ? (M/P)

For each country, in the year 2015, calculate the following:

(a) (4 points) The rate of inflation and the nominal interest rate.

(b) (3 points) The real money supply. Is it true that a higher nominal money supply implies a higher real money supply? Why or why not?

(c) (3 points)The velocity of money

(d) (3 points)The revenue from the inflation tax.

(e) (7 points) Represent the four observations for inflation tax revenue on a graph with the inflation rate on the horizontal and the inflation tax revenue on the vertical axis. Given the shape of the graph, would you say that the relationship between the rate of inflation and the inflation tax revenue is very different from the relationship between other tax rates and their tax revenues? Is it always possible to increase revenue by hiking tax rates? Explain.

and maximize with respect to ? .

P_2014

P_2015

M_2015

Developed Land

100

101

251,288

Seventies Land

100

110

271,304

Bolivarian Republic

100

200

450,080

Weimar Republic

100

1100

99,440

The inflation tax Consider the following information about the price level P in the years 2014 and 2015 and the money supply M in 2015 for four hypothetical countries

Explanation / Answer

In the year 2015

A) FOR Developed land ( country A)

a. rate of inflation =( Price in 2015 - price in 2014 / price in 2014)*100

=( 101 - 100 / 100)*100 = (1/100)*100 = 1%

b. Nominal interest rate = infltion rate + real interest rate = 1 + 4 = 5%

FOR Seventies land (country B)

a. infaltion = (110 - 100 / 100)*100 = 10 %

b. nominal interest rate = 10 + 4 = 14%

FOR Bolivarian republic ( country C)

a. Inflation = (200 - 100 / 100)*100 = 100 %

b. nominal interest rate = 100 + 4 = 104%

FOR Weimar republic ( country D),

a, Inflation = (1100 - 100 / 100 )*100 = 1000%

b. nominal interest rate = 1000+ 4 = 1004%

B) a. FOR country A

Real money supply = M/P = 251288/ 101 = 2488

For country B

M/P = 271304 / 110 = 2466.4

FOR country C

M/P = 450080 / 200 = 2250.4

FOR country D, M/P = 99440/1100 = 90.4

- No, a higher nominal money supply doesn't imply a high real money supply. A higher money supply can also result to a lower real money supply if prices increase by a ,much larger percentage.

C) Velocity of money (v)= P*Y / M

FOR COUNTRY A, v = 50000* 101 / 251288 = 20.1

FOR B, v = 50000*110 / 271304 = 20.27

FOR C, v = 50000*200 / 450080 = 22.21

FOR D, v = 50000*1100 / 99440 = 553.097

D) The revenue from the inflation tax = inflation * (M/P)

FOR A , = 1* 2488 = 2488

FOR B = 10 * 2466.4 = 24664

FOR C = 100 * 2250.4 = 225040

FOR D = 1000* 90.4 = 90400

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