Part 1: Solow in Solow’s words

Read Technical Change and the Aggregate Production Function (Solow, 1957). This is a pretty tough paper for undergrads, but I have faith that you will be able to manage it. You’ll need to read it several times. On a first reading, don’t let yourself get too stuck with the mathematics. On second/third readings, you should spend time to make sure you understand the model. It is an extremely important paper—it more or less kicked off all of contemporary macroeconomics, and Solow won the 1987 Nobel for his efforts.

Questions:

  • What is Solow’s point?
  • What does Solow mean by neutrality? What is Hicks Neutrality? What is Harrod Neutrality?
  • Is his model different to the one we talked about in class?
  • What data does he use to test his hypothesis?
  • Does Solow find a constant rate of technological progress in the United States?
  • Does Solow find technological progress to be neutral?
  • What does chart 4a show?
  • What is “saturation”?

Question 2: Simulating shocks in a Solow model

This question is quite similar to last week’s programming homework. Your task is write a small Solow model. You will project GDP per worker under two scenarios—the first is a baseline scenario, and the second is one in which the savings rate changes in period 2.

Steps

  • Initialise the exogenous parameters for the baseline model: The savings rate is 25%, depreciation rate is 5%, population growth rate is 2%, capital share of income is 40%, and GDP comes from a Cobb-Douglas production function \(Y_{t} = K_{t-1}^{\alpha}L_{t}^{1-\alpha}\). This is a closed economy (savings = investment).
  • Derive the steady state capital per worker and output per worker analytically.
  • Initialise two variables, capital per worker \(k\) and output per worker \(y\); these should be 200 periods long. (Hint: use rep(NA, 200))
  • Initialise \(k_{1} = 1\) and simulate the model forwards (updating capital and output) 200 periods. Does it converge?
  • Now initialise \(k_{1}\) to be equal to the steady state value that you derived above. Simulate again. Any difference?
  • Now initialise three new series called k1, y1, and s1, where the first two are capital and output per worker, and s1 is a series of savings rates. The first element of s1 is 0.25 (the same savings rate as above). But from the second period onwards, the savings rate is 0.3. Simulate this model.
  • Generate a time-series plot that contains y and y1. (Hint: create a data frame that contains y and y1, and use plot.ts(yourdataframe))

For a bonus mark: - Re-do all the above, introducing labour-augmenting technical change that grows at a rate of 1.5% per year.