Consider the standard Solow model. The expression for output and the dynamics of capital are given by the following expression: Y = AKQL1_' AKstK Where 6 > 0 (constant) is the depreciation rate of capital, .3 is savings rate of a country (also constant). Assume labor is xed at L. (a) Using a Solow diagram, show the steady state level of capital. (label the xaxis and functions that you plot and mark the steady state level of capital) (8 points) (b) Find an algebraic expression for the steady state capital per worker. Show your steps. (c) Suppose a country is in steady state. An unfortunate event kills a signicant portion of the labor force. Assume this is a permanent reduction in labor force. Using the Solow-diagram, explain what happens to the growth rate of output in the economy in the shortrun? What happens to the level of output in the long-run? (10 points) (Hint: your answer should include an explanation with the Solow diagram plot) ((1) What if the onetime shock had destroyed capital stock instead of a reduction in labor force? ( 6 points)