Question

2 - What factors determine the slope of the required investment line? [1 mark] Using Figure 12-2 from the Chapter 12 lecture notes, show the effects of an increase in the rate of technological progress on the Solow growth model. [2 marks] Clearly label your graph.

Answer 1

1. The slope of the Investment- savings curve (or IS curve) is the marginal propensity to invest and is determined by the interest sensitivity coefficient. A high interest sensitivity results in a more gradual slope. In this case, a relatively small reduction in the interest rate, would lead to a drastic increase in investment spending because of the higher sensitivity. The slope depends on changes in income and investment levels.

2. Technological progress improves the efficiency of labour, the new production function may now be expressed as

Y = F(K, L x E)

where E is efficiency of the labour force. With an improvement in technology, the efficiency of labour rises.

An increase in the efficiency of labour (E) has the same effect on output as increases in the labour force (E). Their product (L x E) measures the number of effective workers. So total product (y) now depends on the number of units of capital (K) and the number of effective workers (L x E), where E measures the efficiency of each worker.

The effect of technological progress is the same as that of population growth because it is labour-augmenting in nature.

k = K/(L x E) or capital per effective worker,

and y = Y/(L x E) or output per effective worker.

If the efficiency of labour is growing, then k and y refer to quantities per effective worker.

Δk = sf(k) – (δ + n + g)k

With technological progress, increases in the number of effective workers tend to decrease k. In the steady-state, investment i = sf(k) fully offsets the reduction in k caused by depreciation, population growth and technological progress, i.e.,

Sf(k) = δk + nk + gk

k) 7

g' is the increase in rate of technological growth which is why the break even investment line shifts up. k"* decreases from k*