Question

From the companion website for chapter 4, complete Problem Set B, Question 9: Henry Dan is a researcher for Hugo University, a small private school in Wego, Ohio. Using regression analysis, he estimated the following demand equation for enrollment at Hugo. QX = 94 - 50PX + 8PE + 6PS + 5I + 15R + 3N + 20G Dr. Dan determined that the number of new freshman entering Hugo in the fall (QX) depends on the annual tuition and housing costs at Hugo measured in $1,000s (PX), the annual tuition and housing costs at Eyego College (PE) and Wego State University (PS ), Hugo’s chief competitors for local students, measured in $1,000s, regional per capita annual income measured in $1,000s (I), the financial aid rebate at Hugo measured as a percentage of tuition revenue (R), the number of students who graduated from local high schools in the previous spring measured in 1,000s (N), and the number of games won in the previous season by Hugo’s football team (G).

Use the estimated demand function given above to solve Problems 9 through 13. (Only need #13 answered)!!

9. Hugo, Eyego, and Wego are currently charging $11,000, $15,000, and $6,000, respectively, for tuition and housing. Per capita income in the region is $11,000 and 90,000 students are expected to graduate from local high schools this spring. Hugo’s financial aid rebate is 25% and the football team won 5 games last season. How many new freshmen should Hugo expect in the fall?

10. Calculate the point price elasticity of demand and marginal revenue under the current conditions. If Hugo wants to maximize revenue, should the annual cost of tuition and housing be increased, decreased, or kept the same?

11. Calculate the point income elasticity of demand. Is attendance at Hugo normal or inferior? Is it a luxury, a necessity, or neither?

12. Calculate the point cross-price elasticity of demand with Eyego’s cost of tuition and housing. Are Eyego and Hugo substitutes or complements?

13. Calculate the remaining elasticities associated with Hugo’s demand function and write out the function in terms of percentage changes.

Answer 1

Given QX = 94 - 50PX + 8PE + 6PS + 5I + 15R + 3N + 20G

Also PX, PE, PS, I, and N are given in $1,000s

Ans 9 Given : PS = $6,000

PE = $ 15,000

PX = $ 11,000

I = $ 11,000

R = 25%

N = 90,000

G = 5

QX = 94 - 50PX + 8PE + 6PS + 5I + 15R + 3N + 20G

QX = 94 - 50(11) + 8(15) + 6(6) + 5(11) + 15(25) + 3(90) +20(5)

QX=94-550+120+360+550+375+270+100

QX= 500

Therefore, Hugo should expect 500,000 new freshmen.

Ans 10 Point price elasticity = e = (dQX/dPX)*(PX/QX) = (-50)*(11000/500000) = -0.22

Marginal Revenue = MR = P{1-(1/e)}

MR = 11000{1+(1/0.22)} = $ 61,000

To maximise the revenue,

QX = 94 - 50PX

PX = 1.88 - QX/50

TR = PX*QX (TR is in $1,000s)

TR = 94PX -50PX²

TR'(PX) = 94-100PX =0

PX = 0.94 = $940

So, to maximise the revenue, Hugo should decrease the annual cost of tuition and housing.

Ans 11

Point income elasticity of demand = (dQX/dI)*(I/QX) = 5(11000/500000) = 0.11

As the point income elasticity is positive, so attendance at Hugo is normal. It is neither a luxury nor a necessity.

Ans 12

Point cross price elasticity of demand with Eyego = (dQX/dPE)*(PE/QX) = 8*(15000/500000) = 0.24

As the cross price elasticity is positive, so Eyego and Hugo are complements.

Ans 13

Point cross price elasticity of demand with PS = % Change in QX/ %Change in PS = (dQX/dPS)*(PS/QX) = 6(6000/500000) = 0.36/5 = 0.72

Point cross price elasticity of demand with R = % Change in QX/ %Change in R = (dQX/dR)*(R/QX) = 15(25/500000)= 0.00075

Point cross price elasticity of demand with N = % Change in QX/ %Change in N = (dQX/dN)*(N/QX) = 3(90000/500000) = 0.54

Point cross price elasticity of demand with G = % Change in QX/ %Change in G = (dQX/dG)*(G/QX) = 20(5/500000) = 0.0002