This problem also uses the example in Table 16-1 (p. 521), except where noted. The flexible accelerator model states that net investment In, equals a fraction, f, of the gap between the desired capital stock K*, and last period€™s capital stock k€“1 , The capital stock in any period equals last period€™s capital stock plus last period€™s net investment. The equations that describe these relationships are
In = f(K* - K-1) and K = K-1 + In-1.
Table 16-1 Workings of the Accelerator Hypothesis of Investment for the Hypothetical Mammoth Electric Company

(a) Assume that f equals 0.5. Calculate the amounts of the capital stock, net investment, and gross investment in periods 1€“5.
(b) Using the example in Table 16-1 and your answer to part a, discuss how net and gross investments differ between the simple and flexible accelerator models.

Period Variable 1. Actual sales (Y) 2. Expected sales 0 10.0 10.0 12.0 12.0 120 120 12.0 10.0 11.0 5 1175 1187 ( 0.5Y1 0.5Y1) 3. Desired stock of electric generating stations 40.0 40.0 44.0 46.0 47.0 47.5 4. Net investment in electric 0.0 0.0 4.0 2.0 1.0 0.5 generating stations 5. Replacement investment 4.0 4.0 4.0 4.4 4.6 4.7 (D 0.10K) 6. Gross investment 4.0 4.0 8.0 6.4 5.6 5.2