Q4
(a)
National income Y currently stands at $20 tn/yr (trillion dollars per year) and
consumption C = C(Y) at $16 tn/yr. If marginal consumption C'(Y) = 0.7,
use the Small Increment Formula to obtain an approximation to the level of
consumption if Y rises by $0.2 tn/yr.
(b)
The general price level P is rising over time according to the formula P(t) =
P_0(exp(at) + bt), where P_0, a, and b are positive parameters. Calculate:
(i)
The rate of increase of prices, \(\dot{P}\) at t;
(ii)
The rate of growth of prices \(\hat{P}\) at t. Then
(iii)
Evaluate both \(\dot{P}\) and \(\hat{P}\) when t = 0.
