Exercise 21.11. Consider the model presented in subsection 21.6.2. Make the following two modifications. First, the utility function is now (21.68) (1 − δ) −(1−δ) δ−δc1−δbδ and second, unskilled agents receive a wage of wu + ε where ε is a mean-zero random shock. (1) Suppose that ε is distributed with support [−ψ, ψ], and show that if ψ is sufficiently close to 0, then the multiple steady states characterized in 21.6.2 “survive” in the sense that depending on their initial conditions some dynasties become high skilled and others become low skilled. (2) Now suppose that ε is distributed with support [−ψ,∞), where ψ ≤ wu. Show that in this case there is a unique ergodic distribution of wealth and no poverty trap (in the sense that every dynasty will become skilled at some point with probabability 1). Explain why the results here are different from those presented in subsection 21.6.2? (3) Why was it convenient to change the utility function from the log form used in the text to (21.68)?