12. Labor pooling. Firms can choose to located in an isolated site or in a cluster, and make this choice to maximize expected profits. Workers can choose to live in an isolated site or a cluster, and make this choice to maximize expected wages. Firms and workers must make this choice before firm-level, idiosyncratic demand shocks are realized. Assume: 1. Labor supply in the cluster is perfectly elastic at a wage of 8. 2. When demand for a given firm's output is high, their inverse demand curve for labor is W (Q) = 23 Q. 3. When demand for a given firm's output is low, their inverse demand curve for labor is W;(Q) = 13 Q. 4. Firms have an equal probability of having high or low demand. 5. Firms take the local wage as given. That is, they do not take advantage of their monopsony power. 6. Firms only variable cost is labor. (a) (4 points) Draw a diagram highlighting the profits of the firm in each of the two markets. Please mark the equilibrium quantity of workers and wages (when demand is high and low) on both figures. (b) (3 points) Please explain why the area you labeled as profits in the cluster when demand is low is correct? (c) (3 points) How many workers choose to live in the isolated site? (d) (3 points) What are expected profits in the isolated site? (e) (3 points) What are expected profits in the cluster? (f) (2 points) Do firms wish to cluster? Why? Your answer should contain numbers but be focused on the intuition (in just 1-2 sentences)