Question

1/ Growth Rates of Capital and Output Consider the following production function: Yt = F(Kt , Lt) = K 1 2 t L 1 2 t Assume that capital depreciates at rate ? and that savings is a constant proportion s of output: St = sYt Assume that investment is equal to savings: It = St Finally, assume that the population is constant: Lt = Lt+1 = L 1. The production function above expresses output as a function of capital and labor (workers). Derive a function that expresses output per worker as a function of capital per worker (i.e. find yt = f(kt)). 2. Write down the capital accumulation equation in terms of capital per worker (i.e. an equation with only kt+1, kt , ?, and s. 3. Solve for the steady state level of capital per worker as a function of ? and s. 4. Solve for the steady state level of output per worker as a function of ? and s. 5. What is the steady state growth rate of output per worker? 6. What is the steady state growth rate of output?

2/ Yt = F(Kt , Lt) = (K 1 2 t + L 1 2 t ) 2 Assume that capital depreciates 5% each year and that households save 5% of their income. Assume that investment is equal to savings. Finally, assume that the population is growing 15% each year. Solve for the steady state level of output per worker.

Answer 1