(Solved): (a) National income Y currently stands at $20tn/yr (trillion dollars per year) and consumption C=C( ...

(a) National income $Y$ currently stands at $\$20\mathrm{tn}/\mathrm{yr}$ (trillion dollars per year) and consumption $C=C(Y)$ at $\$16\mathrm{tn}/\mathrm{yr}$. 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 $\$0.2\mathrm{tn}/\mathrm{yr}$. (b) The general price level $P$ is rising over time according to the formula $P(t)=$ $P_0(\exp (?t)+bt)$, where $P_0,?$, and $b$ are positive parameters. Calculate: (i) The rate of increase of prices, $\stackrel{?}{P}$ at $t$; (ii) The rate of growth of prices $\hat{P}$ at $t$. Then (iii) Evaluate both $\stackrel{?}{P}$ and $\hat{P}$ when $t=0$.