Economics

1. In a neo-classical growth model, production is governed by the production function, y = k1/2,
where y=Y/N and k=K/N are, respectively, output and capital (both expressed per capita). In the
first year of analysis, the economy has an employed labour force of 100,000 and a capital stock
of 1,600,000 units. The growth rate, N, of the labour force is 10%; and the savings rate, s, is
40%. Assume no depreciation and no technological progress
a. Calculate the initial values of y and k. Verify that the economy is on a balanced growth path.
b. Suppose the savings rate rises to 50%. Calculate the values of y, k, actual investment (sy),
and balanced-growth investment (nk) for the next year. (Hint: k1 = k0 + nk0 )
2. Explain what happens to capital and output in the short run and in the long run if the technological
growth rate decreases.