There are 810 identical consumers, each with the following utility function: U, = X/Y; each consumer has Mi = $300. There are 2,000 identical, perfectly competitive firms producing good X, each utilizing the following production function: Xi=2L"K". Assume PL = $18, PK = $5, and K is fixed at 9 units in the short run. Derive the short run (4 pts. each): (a) price (Px ); (b) quantity exchanged in the market (X ); (c) the typical firm's output (xi ); (d) the typical firm's profits (a; ); and (e) the typical consumer's consumption of X (x;*)