Market Demand Curve(9 points) Professor Adams and Brown make up the entire demand side of the market

Market Demand Curve(9 points)
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?
3 Revenue Maximization(15 points)
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. 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?

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