Question

Assume you are an admissions administrator at University of Iowa and you have calculated the demand for an IU education is:

QD IU= 10,000 - 0.25PIU + 0.1M + 0.4PUM + 0.3PHU + 0.2PSU + 0.1PDU

where QD represents the number of IU students, PIU represents IU tuition, M represents student/parent income, PUM represents University of Michigan tuition, PHU represents Harvard University tuition, PSU represents Stanford University tuition, and PDU represents Duke University tuitions.
a. What can you say about University of Iowa demand with respect to income and the prices of other state universities? Explain how you determined each result.

b. What will Iowa demand be if PIU =$6,000, M=$45,000, PUM =$8,000, PHU =$11,000, PSU =$13,000, and PDU =$13,000?

c. Determine the inverse demand function and graph Iowa’s demand curve (be sure to label the axes and relevant intercept values).

d. At the current price, will there be a shortage or surplus of potential IU students if University of Iowa's supply is: QS IU = 2,000 + 3PIU? What is the magnitude of the shortage or surplus? What recommendation would you give to IU pricing administrators to solve this problem? Graphically show how your recommendation solves this problem.

e. What is equilibrium price and quantity? Does the equilibrium price support or reject your answer to part d?

f. Although not reflected in the equations above, what do you think will happen if IU includes advertising as part of their recruiting strategy? Explain/show your result graphically.

Answer 1

Given:

$Q_D(IU) = 10000 - 0.25P_{IU }+ 0.1M + 0.4P_{UM} + 0.3P_{HU} + 0.2P_{SU}+0.1P_{DU}$

a) University of Iowa demand

• w.r.t. income $= \frac{\partial }{\partial M}Q_D(IU) = 0.1$
• w.r.t. tuition of University of Michigan $= \frac{\partial }{\partial P_{UM}}Q_D(IU) = 0.4$
• w.r.t. tuition of Harvard University$= \frac{\partial }{\partial P_{HU}}Q_D(IU) = 0.3$
• w.r.t. tuition of Stanford University$= \frac{\partial }{\partial P_{SU}}Q_D(IU) = 0.2$
• w.r.t. tuition of Duke University$= \frac{\partial }{\partial P_{DU}}Q_D(IU) = 0.1$

b)

If PIU =$6,000, M=$45,000, PUM =$8,000, PHU =$11,000, PSU =$13,000, and PDU =$13,000, then

$Q_D(IU) = 10000 - 0.25*6000+ 0.1*45000 + 0.4*8000 + 0.3*11000+ 0.2*13000+0.1*13000$

$\Rightarrow Q_D(IU) = 10000 - 1500+ 4500 + 3200 + 3300+ 2600+1300 = 23400$

c)

Assuming tuition fee of other universities as given in the previous part,

$Q_D(IU) = 10000 - 0.25P_{IU}+ 0.1*45000 + 0.4*8000 + 0.3*11000+ 0.2*13000+0.1*13000$

$\Rightarrow Q_D(IU) = 10000 - 0.25P_{IU}+ 4500 + 3200 + 3300+ 2600+1300$

$\Rightarrow Q_D(IU) = 10000 - 0.25P_{IU}+ 14900 \Rightarrow Q_D(IU) = 24900 - 0.25P_{IU}$

$\Rightarrow 0.25P_{IU} = 24900 - Q_D(IU) \Rightarrow P_{IU} = 99600 - 4Q_D(IU)$

This is the inverse demand function for Iowa university.

d)

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