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Q1: Consider the problem of a rm that is choosing whether to locate in an isolated town or in a city. If it chooses to locate in a city, then the rm can share the labor pool with a cluster of rms. (3): Suppose there are eight workers in a town available for the rm. The demand function for labor, when demand is low, is Ld = 24 211: (here, w is the wage rate). For this isolated town, when labor demand is low, compute the equilibrium wage using algebra and show it in a diagram. [3 points] (b): In the same isolated town as in part (a) , the labor demand function when demand is high is L3,, = 32210. For this isolated town, when labor demand is high, compute the equilibrium wage using algebra and show it in a diagram. [3 points] (c): Suppose the rm expects demand to be high with 25% probability and demand to be low with prob- ability 75%. Calculate the cluster (city) wage such that locational equilibrium is achieved and show it in a diagram. Explain the intuition behind your calculation. [4 points] ((1): Compute rm prots in the isolated town when: (i) demand is high and (ii) demand is low. [Hint: the area of a right angle triangle is 1/2* base * height]. [4 points] (9): Now, consider the city where there is a cluster of rms. The wage equals the competitive wage from part c. The labor demand functions are as in part (a) and part (b). Compute the number of workers that will be hired in the city when: (i) demand is high and (ii) demand is low. [4 points] (f): Compute rm prots in the city when demand is: (i) high, (ii) low. [4 points] (g): Suppose the rm expects demand to be high with 25% probability and demand to be low with proba- bility 75% in both the isolated town and city. Compute expected prots of the rm if it locates in: (i) the isolated town, and (ii) in the city. [5 points] [Hint: Expected Prots = (Prob that demand is low * prots when demand is low) + (prob that demand is high * prots when demand is high)]. (h): Based on your answer in part g, should the rm locate in the isolated town or in the city?I Why? [3 points]