1
Teory of economic growth
Miguel Lebre de Freitas Mid-term 1 (Oct 31, 2014)
I (4.5 val) Define 3 of the following concepts:
(i) Steady state
(ii) Missing institutions theory of fertility (iii) Growth accounting
(iv) Conditional convergence (v) Human capital
II (13.5 points) Choose 2 of the following exercises:
II.1. Consider a close economy devoted to agriculture, where aggregate production can be described by Yt = BTt0.5Nt0.5. The amount of land available is T=1, and B=50. The population dynamics can be described by the following equation Nt −Nt−1=10
[
yt−1−y]
where y=5 is subsidence per capita income.
Find out the stead state in this economy, (N*, y*) and represent in a graph. Is it a stable steady state? Explain.
Suppose that, at moment t=1, some swamps were drained, so that arable land expanded by 44%. How much would be per capita income in that year? And population in year t=2? How much would be population, per capita income and population density in the long run? Represent in a graph.
Assume that, instead of exogenous, technology was a function of the last year’
populationBt =0.5Nt−1. (c1) Explain the intuition; (c2) Confirm the technological level at moment t=1. (c3) Explain what would happen to technology, per capita income and population in the years that followed the swamp drainage.
II.2. In economy W, the aggregate production function is given by Yt = AtKt1/4Nt3/4, where N refers to population. In this economy, s=24%, n=1%, δ=0, and At =8e0.015t.
Find out the stedy state values of K/L and Y/L, where L is labour in efficiency nits. Represent the equilibrium in a graph and explain why it is stable.
2 Compute the interest rate, the capital and labour income shares, and explain the steady state patterns of wages and per capita income. Are these results in accordance to the Kaldor facts?
Assume that a benevolent planner managed to increase the saving rate in this economy to s=27.78%. (f1) Would the growth rate of per capita income change? (f2) What about the interest rate? (f3) Consumers would be better off? Explain, quantifying when possible.
II.3. Consider and economy P, where the production function in the intensive form takes the following form yt = Atkt1/3ht1/3. It is also known that per capita income in this economy is 21.6% of the corresponding level in the leader economy, R.
If the only difference between P and R was the level of capital per worker, how much should be k in P, as compared to R? And the interest rate? Represent in a graph and explain if your findings are plausible.
Suppose the data revealed k in P to be roughly 21.6% of the corresponding level in R. In that case, the difference in interest rates would be reasonable?
If technology was the same, how much should be the difference in human capital per worker? Is this difference reasonable?
Now assume that human capital per worker in the poor country was exactly 34.3% of that in the rich country. How much should be the difference in technology? Is this reasonable?
What do you conclude from this exercise?
IV (2 val)
Choose one of the two questions:
To which extent industrialization helped explain the demographic transition?
To which extent the neo-classical model with human capital is helpful to understand why some countries are richer than others? What are the main limitations of this model?
