Consider an economy with one consumption good, 100 identical consumers and 100 identical firms. Each consumer is endowed with one unit of time and…

3. Consider an economy with one consumption good, 100 identical consumers and 100 identical firms. Each consumer is endowed with one unit of time and one piece of land. The agent can spend time either working or enjoying leisure. A representative consumer’s utility function is u (x; r) = ln x + ln r, where x is consumption of goods and r is leisure. Each firrm hires consumers to work and rents land from consumers to produce goods: y = f (L; D) = (LD)^(1/2), where L is the amount of labor hired and D is the amount of land rented. Both consumers and firms take goods price p, wage rate w and rent rate q as given. Normalize p* = 1.