Consider the following variation of the usual Solow growth model. Rather than assume that the depreciation rate is a constant, suppose instead that the depreciation rate depends upon capital per worker in the following way: d=d1d=d2ifk>k^ifkk^ where d2>d1 and k^>0 are given. a. Let k1 be the steady-state level of capital per capita when d=d1 and k2 be the steady-state level of capital per capita when d=d2. Assume further that k1>k^>k2. Using a figure similar to Figure 7.13 (but with two "law of motion" functions, one for each value of d ), show that there are there are two strictly positive steady states in this economy. b. Is the low income steady state, k2, stable or unstable? That is, if the economy moves a small distance away from k2, ceteris paribus, does it return to the same steady state? Likewise, is the high income steady state, k1, stable or unstable? c. Does an economy such as this suggest the possibility that a country with a high depreciation rate could be "trapped" in a low-income steady state? Why or why not? Consider the following variation of the usual Solow growth model. Rather than assume that the depreciation rate is a constant, suppose instead that the depreciation rate depends upon capital per worker in the following way: d=d1d=d2ifk>k^ifkk^ where d2>d1 and k^>0 are given. a. Let k1 be the steady-state level of capital per capita when d=d1 and k2 be the steady-state level of capital per capita when d=d2. Assume further that k1>k^>k2. Using a figure similar to Figure 7.13 (but with two "law of motion" functions, one for each value of d ), show that there are there are two strictly positive steady states in this economy. b. Is the low income steady state, k2, stable or unstable? That is, if the economy moves a small distance away from k2, ceteris paribus, does it return to the same steady state? Likewise, is the high income steady state, k1, stable or unstable? c. Does an economy such as this suggest the possibility that a country with a high depreciation rate could be "trapped" in a low-income steady state? Why or why not