Section B: Questions on Course Material
- Growth and Total Factor Productivity:
- a What is total factor productivity (TFP) and how does it affect economic growth? [15]
- b What is the Golden Rule, and does it seem plausible? [10]
- c “Growth always leads to more inequality; do we really want more growth then?” Do you agree with this statement? [10]
- a Needs definition of TFP:
- Portion of output not explained by the amount of inputs used in production.
- Affects growth in that it is all sorts of difficult to measure and conceptualise factors that lead to some countries growing more strongly than others — human capital, institutions (e.g. trust).
- b Definition important again:
- Investment level consistent with maximising steady-state consumption level with respect to capital stock.
- More investment not necessarily better: Foregone consumption.
- Ignore \(G\) and \(NX\) so \(Y=C+I\) and hence \(C=Y-I\).
- In steady state \(I=dK\), hence \(C^{ss}=Y-dK\).
- Care about: \(\frac{\partial C^{ss}}{\partial K} = \frac{Y}{K}-d = 0\) hence \(MPK - d=0\).
- Golden Rule: MPK must equal depreciation rate.
- Cobb-Douglas production function: \(Y=TFP\times K^\alpha L^{1-\alpha}\). Plausible???
- Differentiating by \(K\) gives: \(MPK = \frac{\alpha Y}{K}\).
- Golden Rule says \(MPK=d\) hence \(d=\frac{\alpha Y}{K}\).
- Recall we assume investment fixed proportion of output: \(I=bY\). Plausible???
- Hence in steady state \(I=bY=dK\) and so \(d=\frac{b Y}{K}\).
- Implying \(\alpha=b\) for Golden Rule:
- Investment at around capital’s share of national income \(\approx 0.3\).
- c Good to reiterate definition of inequality:
- Note specific to income here; definition of inequality need not be income inequality!
- Analysis from lecture useful here.
- Dissect statement:
- Growth does not always lead to inequality. It might sometimes.
- Even if it does lead to inequality, growth still desirable if all are better off?
