ECO202
Extra Question F6
1. This question relates to the Solow growth model discussed in Chapter 5. Mont Plaisant, a closed economy with no government spending, operates under the following production function:
In this model, Yt represents the output in period t, Kt denotes the capital stock in period t, and Lt stands for the labor employed in period t. The accumulation of capital follows the standard equation:
where δ is the depreciation rate and It is the investment in period t.
Mont Plaisant’s population saves a fixed proportion, , of their output for investment each period. The population grows at a rate , following the equation Lt+1 = (1 + )Lt . Lowercase letters represent per-person values of the variables.
(a) Convert the capital accumulation equation from aggregate to per-person terms. The left-hand side should equal ∆kt+1, while the right-hand side should include y t , kt , and the relevant parameters.
(b) Find the steady-state values of capital per capita (k*) and output per capita (y*).
(c) What happens to output per capita in the steady state when increases? Use your findings from part (b) to explain.
(d) Another economy, Mont-Tremblant, has similar characteristics (i.e., identical parameters) but currently has lower output than Mont Plaisant. Meanwhile, Mont Plaisant is in its steady state. How should we expect the growth rate of output in Mont-Tremblant to compare to that of Mont Plaisant? Why? Explain in 2-4 sentences.
(e) Draw a Solow diagram with k on the x-axis to illustrate the scenario described in part (d).
(f) Draw two separate time graphs (on a ratio scale) for Y and y, one for Mont Plaisant and the other for Mont-Tremblant.