Consider the one-sector Schumpeterian model in discrete time analyzed in the previous exercise, except that now (.) denotes the probability of innovation, and each innovation improves the quality of a machine q to λq, where λ > 1. Suppose that when a new innovation arrives a fraction ϕ of workers employed in the final good production are unable to adapt to this new technology and need to remain unemployed for one time period to “retool.” (a) Define the equilibrium and steady-state (BGP) allocations. [Hint: also specify the number of unemployed workers in equilibrium.] (b) Define the appropriate generalization of the steady state for this economy, and determine the number of unemployed workers in this equilibrium. (c) Show that the economy experiences bursts of unemployment followed by periods of full employment. (d) Show that a decline in ρ increases the average growth rate and the average unemployment rate in the economy.
Consider the one-sector Schumpeterian model in discrete time analyzed in the previous exercise, except that now 
(.) denotes the probability of innovation, and each innovation improves the quality of a machine q to λq, where λ > 1. Suppose that when a new innovation arrives a fraction ϕ of workers employed in the final good production are unable to adapt to this new technology and need to remain unemployed for one time period to “retool.”
(a) Define the equilibrium and steady-state (BGP) allocations. [Hint: also specify the number of unemployed workers in equilibrium.]
(b) Define the appropriate generalization of the steady state for this economy, and determine the number of unemployed workers in this equilibrium.
(c) Show that the economy experiences bursts of
(d) Show that a decline in ρ increases the average growth rate and the average unemployment rate in the economy.
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