Question

1.Professor Adams and Brown make up the entire demand side of the market for summer research assistants in the economics department. If Adams’s demand curve is P = 50 − 2QA and Brown’s is P = 50 − QB, where QA and QB are the hours demanded by Adams and Brown, respectively, what is the market demand curve for research hours in the economics department?

2.Umass Amherst is committed to its current policy of allowing the children of its faculty to attend the university without paying tuition. Umass Amherst plans to admit Q¯ students in the coming academic year. Suppose the demand curve of Umass Amherst faculty children (UFCs, currently q such children applying for college) for slots in other universities is given by P = 30 − 5Q0, where P is the tuition price charged by other universities (in thousand of dollars) and Q0 is the number of UFCs who attend those universities. Umass Amherst is now considering a proposal to subsidize some proportion k of the tuition charged to UFCs who attend other universities. Suppose Umass Amherst knows that it can fill all its available slots with non-UFCs who pay tuition at the rate of $45,000/yr. Assuming that all UFCs who do not attend other universities will go to Umass Amherst, what value of k will maximize Umass Amherst’s tuition revenues, net of outside subsidies, if the tuition price at all other universities is $24,000/yr?

Answer 1

1. To calculate the market demand, we will convert the individual inverse demand functions to direct demand functions.

Adam's inverse demand function: P = 50 − 2*QA

This means, QA= (50 - P)/2 = 25 - P/2

Brown’s inverse demand function: P = 50 − QB

This implies, QB = 50 - P.

The total market demand is the sum of individual demand functions-
Market demand curve (QM) = QA + QB

=> QM = (25 - P/2) + (50 - P)

Therefore, the market demand curve for research hours in the economics department is