Part 1 : Solow in Solow’s words

  1. What is Solow’s point?

Solow’s point is that, assuming factors are paid their marginal products, it is possible to isolate shifts of the aggregate production function from movements along it. In other words, it is possible to observe the affects of technical change on output per head than those caused by changes in the availability of capital per head. The effect of shifts (technical change) over time is denoted by the multiplicative factor A(t) in the production function.

  1. What does Solow mean by neutrality? What is Hicks Neutrality? What is Harrod Neutrality?

When he mentions neutrality, Solow is referring to neutral technical change. This is a case in which technical change (also known as a shift in the production function) increases or decreases output attainable from given inputs whilst leaving marginal rates of substitution unaffected. Harrod and Hicks neutrality also refer to neutral technical change. Hicks neutrality involves technical progress in which the average and marginal products of inputs both increase in the same proportion. Harrod neutrality concerns the input of labour, wherein technical progress increases the average and marginal product of labour.

  1. Is his model different to the one we talked about in class?

This paper focuses on growth accounting and productivity slowdown which performed a simple accounting exercise to break down growth in output in growth in capital, growth in labor, and growth in technological change. While the model in class focus on how differences in investment rate and population growth rate and technological progress (exogenous) effect sustained growth of economics.

  1. What data does he use to test his hypothesis?

In testing his hypothesis Solow uses data on the US covering the period from 1909 to 1949. This data displays the percentage of the labor force employed, the value of capital stock, share of property in income, Gross National Product per man-hour (private, non farm activity) and employed capital per man-hour. This data was derived from a range of sources.

  1. Does Solow find a constant rate of technological progress in the US?

Solow finds the trend of technological progress to appear to grow from 1909 to 1949. In saying this, the first 21 years grow at a much smaller rate (0.09%) in comparison to the latter 19 years average of 2.25% growth, with the combined average of 1.5% growth per year. However, Solow noted a strong downward shift in 1929 which may amplify the difference between the two periods.

  1. Does Solow find technological progress to be neutral?

During the period of 1909 to 1949 Solow states that there is no trace of a relationship between capital and labour. In doing this, he concludes that the aggregate production is approximately neutral.

  1. What does chart 4a show?

The chart 4 shows a scatter of q/A against k of aggregate production function on a different member of the family of production. Solow point out the layer of points which are obviously too high relate to the seven last years of the period, 1943-49. The possible explanation he suspected that might be some systematic incomparability of the capital-in-use series. In particular during the war there was almost certainly a more intensive use of capital services. Even though, it is unlikely that this could be nearly enough to explain the whole discrepancy. Chart 4 gives an inescapable impression of curvature, of persistent but not violent diminishing returns. After a few test seems to be left to their just cause the distortion of the obvious results.

  1. What’s saturation?

Saturation is the point at which gross marginal product falls to the marginal rate of depreciation. This suggests that an increase in capital from this point will only move to depreciate the product to the level of the investment.

Part 2 : Simulating shocks in a Solow model 

s<- 0.25
delta<- 0.05
n<- 0.02
alpha<- 0.4
k <- (s/(delta+n))^(1/(1-alpha))

Steady State

\[ k = \left(\frac{s}{\delta + n} \right)^\frac{1}{1 - \alpha} \]

k
## [1] 8.344557

Solow Model Steady State 

K<- rep(NA,200)
K[1]<- 1

Y<- rep(NA,200)
c <- delta + n

for (t in 2:200)
  {Y[t]<- K[t-1]^alpha
  K[t]<- (1-delta-n)*K[t-1]+s*Y[t]}

plot.ts(K)

Beginning at Steady State Value 

K<- rep(NA,200)
K[1]<- k

Y<- rep(NA,200)
c <- delta + n

for (t in 2:200)
  {Y[t]<- K[t-1]^alpha
  K[t]<- (1-delta-n)*K[t-1]+s*Y[t]}

plot.ts(K)

Savings rate of 2.5% for 1 period, then 3% after 

k1 <- rep(NA,200)
y1 <- rep(NA,200)
s1 <- rep(0.3,200)
s1[1] <- 0.25
k1[1] <- 1
y1[1] <- 1

for (t in 2:200) {
    y1[t] <- k1[t-1]^alpha
    k1[t] <- (1-delta-n)*k1[t-1]+s1[t]*y1[t]
}

plot.ts(k1)

yMap = data.frame(Y,y1)
plot.ts(yMap)