Solow modelSuppose output per worker can be described by the per worker production function yt = Aka. We assume that there is no population growth (L is constant). On average each worker saves a fraction ? ? (0, 1) of her output. In a closed economy, savings equal investments, thus, the amount of investment that is added to the per capita capital stock is it = ?yt. Each year, a share d of the capital stock is lost due to depreciation, i.e. dt = dkt.

a) Write down the capital accumulation equation per worker, i.e. how the capital stock per worker evolves from t to t + 1.

b) Plot y, i, and d as functions of k together in one graph. Label the steady state capital stock with k* and the corresponding output y*.

c) Find the growth rate of capital per worker in the steady state.

d) Find the expression for the steady state capital stock per worker (k*) as a function of the parameters ?, A, d, and a. (Hint: use the condition for the steady state.) Insert this expression in the production function to get an expression for output per worker in the steady state (y*).

e) Assume the economy currently has a capital stock per capita below its steady state level: k

f) Make a new graph with time on the horizontal axis and k on the vertical. At time t0 the capital stock is as before k0

g) Assume that two countries A and B have the same production function, saving rate and depreciation rate. Country A is in the steady state, but country B is below the steady state. What can you say about the growth rates of these two countries over time?