Question

1. In the French town of Louisbourg, (now part of Nova Scotia), in 1757, the aggregate production function per worker was y = Ak^0.75. Louisbourg’s workers save a fraction, s, of their incomes, so aggregate savings is given by S = sY.
1a. If the savings rate, population growth, depreciation rate and productivity are: s = 0.25, n = 0.15, d = 0.10, A = 4, then what was the steady-state capital-labour ratio k* and k^Golden. Given k*, what are steady-state output per-worker, y*, steady-state consumption perworker, c*, and steady-state investment per-worker, i*? (No figure required) (9 Marks)
1b. The British captured Louisbourg and in 1760 destroyed part of the buildings (capital) so k is now 100. Assuming this did not impact A, n, s or d, how would your answer differ from 1a? Describe and show calculations of what is occurring over time and link your description to a figure. What would happen instead if the British had built buildings and increased k to 400? (Figure does not have to be to scale.) (10 Marks)   


2. The production function for Canada in 2014 is Y= A(25N-2N^2) + 5N^2, where Y = Output, A = total factor productivity, N = labour and K = capital.

i) Using calculus, derive an expression for aggregate labour demand (N^D). (3 points)

ii) If N^S = 50 + 0.125w, find the equilibrium wage, w* when A=2 and K=10. (3 points)

Answer 1

The equation for the production per worker is given as:

According to the Solow model, there is no change in the capital stock at the steady state equilibrium level.

At steady state equilibrium,

The condition for the golden rule level of the capital stock per worker is given as follows:

Thus, the value of the golden rule capital stock per worker is 20,736.

The steady state output per worker is determined by substituting the value of k in the production function equation. Thus, the value of steady state output per worker is determined as follows:

The consumption function equation is determined by taking the difference between income and the saving.

At steady state, the saving is equal to the investment.