The production function is Y = AKL-a (1) where L is labor at time t, K,...

 

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The production function is Y = AKL-a (1) where L is labor at time t, K, is capital at time t, A, is TFP at time t and a (0, 1). The law of motion for capital is K = 8Y-8K Assume that TFP evolves endogenously: (2) A = ONE (3) where N is total population. Also assume that labor is a constant fraction of total population: L = hN Population grows at a constant rate of n = Nt Nt (4) (5) (a) What is the definition of a balanced growth path (BGP)? (b) Show that on any BGP, it must be that where gy 9y=9K = 9 Y/Y is the growth rate of output and gk = K/K is the growth rate of capital. (c) What kind of economic phenomenon may be represented by an equation like (3)? The production function is Y = AKL-a (1) where L is labor at time t, K, is capital at time t, A, is TFP at time t and a (0, 1). The law of motion for capital is K = 8Y-8K Assume that TFP evolves endogenously: (2) A = ONE (3) where N is total population. Also assume that labor is a constant fraction of total population: L = hN Population grows at a constant rate of n = Nt Nt (4) (5) (a) What is the definition of a balanced growth path (BGP)? (b) Show that on any BGP, it must be that where gy 9y=9K = 9 Y/Y is the growth rate of output and gk = K/K is the growth rate of capital. (c) What kind of economic phenomenon may be represented by an equation like (3)?