Answer to Question #304283 in Microeconomics for nana

Question

1.    Assume that in 2018 only 1,000 UHV students sign up for the 1,500 positions in UHV residence halls at a set contract price of $3,000 per year.

 

a.    If UHV lowers the contract price to $2,500/year and 500 more students sign up, what is the price elasticity of demand for residence hall positions? You must show your work.

b.    Depict the situation on a supply and demand graph. Be sure to label your graph.

c.    With the information about demand elasticity, if the university president asked for your advice, would you recommend the price be cut, or not?

Answer 1

a)

price elasticity of Demand (PED) $= \frac {\%\Delta\space in\space Quantity\space Demand}{\%\Delta\space in \space Price}$

Q₀ =1,000 P₀ =3,000

Q₁ =1,500 P₁ =2,500

$PED= \frac{{(1,500-1,000)}\space\div\space{(1,500+1,000)}} {{(2,500-3,000)}\space\div\space{(2,500+3,000)}}$

$=\frac {500}{2,500}\space\div\space \frac {-500}{5,500}$

$= 0.5\space\div\space-0.09$

$=-5.5$

b)

when the price falls from P₀ to P₁ the quantity demand increases from Q₀ to Q₁

c)

I would recommend the price not to be cut since the relationship shown above is inverse. If the price is increased the quantity demanded will decrease leading to reduced revenue earned from the residence halls.