Suppose we have an aggregate production function, Y= zKN^(1-), where 0 < <1. Households save a constant fraction s of their income. This implies that aggregate investment is given by I = sY. The capital stock depreciates at the rate 0 < d< 1. Suppose population grows at the constant rate, n.

A. Derive the law of motion equation for the capital stock per worker (how tomorrow's capital stock per worker relates to today's capital stock per worker and other parameters), and solve for the steady state capital stock per worker k*.

B.Suppose there is a childcare subsidy policy that increase the population growth rate immediately. Graphically show what happens to the capital stock per worker immediately and in the long run as a result of this policy. In addition, please plot what happens to the growth rate in output per capita over time, and what happens to the level of output per capita over time.