A linear production function Consider the production function Y = AK + BL, where A and B are positive constants.
a. Is this production function neoclassical? Which of the neoclassical conditions does it satisfy and which ones does it not?
b. Write output per person as a function of capital per person. What is the marginal product of k? What is the average product of k? In what follows, we assume that population grows at the constant rate n and that capital depreciates at the constant rate δ.
c. Write down the fundamental equation of the Solow-Swan model.
d. Under what conditions does this model have a steady state with no growth of per capita capital, and under what conditions does the model display endogenous growth?
e. In the case of endogenous growth, how does the growth rate of the capital stock behave over time (that is, does it increase or decrease)? What about the growth rates of output and consumption per capita?
f. If s = 0.4, A = 1, B = 2, δ = 0.08, and n = 0.02, what is the long-run growth rate of this economy? What if B = 5? Explain the differences.