Question

(11.7) Let the demand for money in the economy be given by 150,000 - [Inflation (%)] 3 . Calculate the amount of revenue raised through the inflation tax for inflation rates up to 50% (a spreadsheet would help!). What inflation rate maximizes revenue?

Answer 1

Given that the demand for money = 150,000 - [Inflation (%)^3]

inflation tax is given by = (inflation/100) x (150,000 – (% inflation)^3 = 1500 x inflation % - (inflation %)^4/100

For inflation rates 0% to 50%, we find the schedule of money demand and inflation tax. Find the optimum / revenue maximizing inflation tax by finding the derivative of the tax function and equating it equal to 0

1500 - 4*inflation%^3/100 = 0

150000/4 = inflation%^3

This gives the revenue maximizing inflation tax = 37500^1/3 = 33.47%.

Inflation rate	Money demand	Inflation tax
1	149999	1499.99
2	149992	2999.84
3	149973	4499.19
4	149936	5997.44
5	149875	7493.75
6	149784	8987.04
7	149657	10475.99
8	149488	11959.04
9	149271	13434.39
10	149000	14900
11	148669	16353.59
12	148272	17792.64
13	147803	19214.39
14	147256	20615.84
15	146625	21993.75
16	145904	23344.64
17	145087	24664.79
18	144168	25950.24
19	143141	27196.79
20	142000	28400
21	140739	29555.19
22	139352	30657.44
23	137833	31701.59
24	136176	32682.24
25	134375	33593.75
26	132424	34430.24
27	130317	35185.59
28	128048	35853.44
29	125611	36427.19
30	123000	36900
31	120209	37264.79
32	117232	37514.24
33	114063	37640.79
34	110696	37636.64
35	107125	37493.75
36	103344	37203.84
37	99347	36758.39
38	95128	36148.64
39	90681	35365.59
40	86000	34400
41	81079	33242.39
42	75912	31883.04
43	70493	30311.99
44	64816	28519.04
45	58875	26493.75
46	52664	24225.44
47	46177	21703.19
48	39408	18915.84
49	32351	15851.99
50	25000	12500