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)