the standard Solow model. The expression for output and the dynamics of capital are given by the following:

Y=AK^rL^1-r

K = sY-K

where > 0(constant) ) is the depreciation rate of capital, s is savings rate of a country (also constant). Assume labor is fixed at L.

1a) Using a Solow diagram, show the steady state level of capital. (please also label the x-axis and functions and mark the steady state level of capital)

1b)Find an algebraic expression for the steady state capital per worker.(show steps)

1c) Let's say a country is in steady state. An unfortunate event kills a significant portion of the labor force. IF this is a permanent reduction in labor force. Please use the Solow-diagram to explain what happens to the growth rate of output in the economy in the short-run? What happens to the level of output in the long-run?

1d) What if the one-time shock had destroyed capital stock instead of a reduction in labor force?