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  3. 4 cosider a firm that produces a certain good the...

Question: 4 cosider a firm that produces a certain good the...

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4. cosider a firm that produces a certain good. The demand is uncertain. There is 50% chance the demand is high, and 50% chance the demand is low. When the demand is high, its demand for labor is w- 12 -0.5L. When the demand is low, its demand for labor is w 8 - 0.5L. Here uw is wage for each worker and L is the total number of workers it hires. When the demand is high, the profit of the firm can be expressed as (12-a) × L/2; when the demand is low, the profit of the firm can be expressed as (8 w) x L/2 (review slides for why this is the case) The firm considers to locate in one of the two cities. City A is small and only has 8 workers. These 8 workers have perfectly inelastic supply of labor (employment is constant, but wage cain change). City B is big and has many workers. The labor supply is perfectly elastic, which means that all workers work at a given wage no matter whether the demand is high or low a. If the firm decides to locate in city A. If the demand is high, how many workers does the firm hire? What is the wage? How much is firms profit? How about when the demand is low? (10 pts) b. What is the firms expected profit in city A? What is the workers expected wage? (5 pts) c. Workers are freely mobile between the two cities. The fact that both cities have some workers means that the expected wage is the same in both cities. What is the wage in city B? (5 pts) d. If the firm decides to locate in city B. If the demand is high, how many workers does the firm hire? What is the wage? How much is firms profit? How about when the demand is low? (10 pts) e. What is the firms expected profit in city B? Which city will the firm choose to locate? (10 pts)

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