Assume that valley forge hospital has only the following three payer groups: number of average revenue variable cost payer admissions per admission per admission penncare 1,000 $5,000 $3,000 medicare 4,000 $4,500 $4,000 commercial 8,000 $7,000 $2,500 the hospital’s fixed costs are $38 million. a. what is the hospital’s net income? b. assume that half of the 100,000 covered lives in the commercial payer group will be moved into a capitated plan. all utilization and cost data remain the same. what pmpm rate will the hospital have to charge to retain its part a net income? c. what overall net income would be produced if the admission rate of the capitated group were reduced from the commercial level by 10 percent? d. assuming that the utilization reduction also occurs, what overall net income would be produced if the variable cost per admission for the capitated group were lowered to $2,200?

Suppose that two firms produce differentiated products and compete in prices. as in class, the two firms are located at two ends of a line one mile apart. consumers are evenly distributed along the line. the firms have identical marginal cost, $60. firm b produces a product with value $110 to consumers.firm a (located at 0 on the unit line) produces a higher quality product with value $120 to consumers. the cost of travel are directly related to the distance a consumer travels to purchase a good. if a consumerhas to travel a mile to purchase a good, the incur a cost of $20. if they have to travel x fraction of a mile, they incur a cost of $20x. (a) write down the expressions for how much a consumer at location d would value the products sold by firms a and b, if they set prices p_{a} and p_{b} ? (b) based on your expressions in (a), how much will be demanded from each firm if prices p_{a} and p_{b} are set? (c) what are the nash equilibrium prices?