FConsider the Solow growth model, where population grows at the constant rate n, N´=(1+n)N, s = saving rate, the production function is given by Y=zF(K,N), the evolution of capital is given by K´=(1-d)K+I where d = depreciation rate and I = investment. The income expenditure identity is given by Y = C+I and S=I. Please upload pictures of your graphical analysis.
Derive the equation for future capital in per worker terms, expressing it in terms of current capital (k), the population growth rate (n) and the depreciation rate (d) using the information given above.
Given that in steady state all aggregate variables grow at the rate of n, using your answer in (a) derive the equation that expresses the steady state solution to the model and graph it. Clearly label your graph and indicate (k*).
What is the key result of the Solow model, show graphically and explain in words.
What is the golden rule level of capital per worker in the steady state? Show this using the consumption function and explain in words.
Consider an increase in the population growth rate, n. What is the equilibrium impact on capital per worker and output per worker? Show this graphically and using algebraic expressions