Learning-by-doing with microeconomic foundations. Consider a variant of the model in equations (3.22)–(3.25). Suppose firm i’s output is Yi(t) = Ki(t) α[A(t)Li(t)]1−α, and that A(t) = BK(t). Here Ki and Li are the amounts of capital and labor used by firm i and K is the aggregate capital stock. Capital and labor earn their private marginal products. As in the model of Section 3.5, the economy is populated by infinitely lived households that own the economy’s initial capital stock. The utility of the representative household takes the constant-relative-risk-aversion form in equations (2.1)–(2.2). Population growth is zero.

(b) What must the growth rate of consumption be in equilibrium? (Hint: Consider equation [2.21].) Assume for simplicity that the parameter values are such that the growth rate is strictly positive and less than the interest rate. Sketch an explanation of why the equilibrium growth rate of output equals the equilibrium growth rate of consumption.

(c) Describe how long-run growth is affected by:

(d) Is the equilibrium growth rate more than, less than, or equal to the socially optimal rate, or is it not possible to tell?

 

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