Exercise 2.13. Consider the Solow model with non-competitive labor markets. In particular, suppose that there is no population growth and no technological progress and output is given by F (K, L). The saving rate is equal to s and the depreciation rate is given by δ. (1) First suppose that there is a minimum wage w¯, such that workers are not allowed to be paid less than w¯. If labor demand at this wage falls short of L, employment is equal to the amount of labor demanded by firms, Ld. Assume that w>f ¯ (k∗) − k∗f0 (k∗), where k∗ is the steady-state capital-labor ratio of the basic Solow model given by f (k∗) /k∗ = δ/s. Characterize the dynamic equilibrium path of this economy starting withsome amount of physical capital K (0) > 0. (2) Next consider a different form of labor market imperfection, whereby workers receive a fraction β > 0 of output in each firm as their wage income. Characterize a dynamic equilibrium path in this case. [Hint: recall that the saving rate is still equal to s].