Question

The following relations describe monthly demand and supply for a computer support service catering to small business:

Qd = 1,500 – 5 P

Qs = -500 + 5 P

Where Q is the number of business that need services and P is the monthly fee, in dollars

Find the equilibrium price/output level

Calculate point elasticity of demand for this demand function. Is it elastic, inelastic or unitary elastic?

Calculate the Total Revenue at the equilibrium price

Answer 1

At equilibrium

$Qd=Qs$

$1500-5p=-500+5p$

Hence

$1500+500=5p+5p$

$2000=10p$

$p=2000/10=200$

Therefore

Equilibrium price = 200 dollars

Equilibrium output level is, $Qd=1500-5p=1500-(5)200=500$

Point elasticity of demand (E_d) is given by $\Delta Qd /\Delta p$

Let’s assume that if the monthly fee changes from $100 (P0) to $200 (P1), number of business that need services falls from [1500-5(100)]=1000 (Qd0) to [1500-5(200)] = 500(Qd1).

Hence $E$_d$=\Delta Qd/ \Delta p$

E_d= (1000-500)/(200-100)= 2.5

Hence elasticity is unitary elastic for it's greater than 1

Total Revenue at the equilibrium price is

(equilibrium output level x equilibrium Price )

Hence

(500x200) = $100000