2. There are 100 identical consumers and 20 identical rms. Each con sumer is endowed with one unit of time. A representative consumer's utility function is u (:L', r) 2 21mm +1117", where A > 0 is a constant, a: is consump tion of goods and 'r is leisure. Each rm hires consumers to produce goods according to the function y = 4%, where L denotes the labour input. All consumers own equal shares of all rms. Goods price p, wage rate 111, and dividend income are all taken as given. Normalize the goods price p = 1. (a) [5 points] Derive the Marshallian demand function, :3 (10, D) and 7" (10,13), Where D is dividend. (b) [10 points] Derive the rm's input demand function L (w) and prot function 7r (w). (c) [10 points] Write down all the market-clearing conditions. (d) [10 points] Calculate the equilibrium 'wage rate 111*