Answer to Question #138297 in Microeconomics for yousef

Question #138297
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
1
Expert's answer
2020-10-15T03:39:32-0400

At equilibrium

Qd=QsQd=Qs

15005p=500+5p1500-5p=-500+5p

Hence

1500+500=5p+5p1500+500=5p+5p

2000=10p2000=10p

p=2000/10=200p=2000/10=200

Therefore

Equilibrium price = 200 dollars


Equilibrium output level is, Qd=15005p=1500(5)200=500Qd=1500-5p=1500-(5)200=500




Point elasticity of demand (Ed) is given by ΔQd/Δp\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 EEd=ΔQd/Δp=\Delta Qd/ \Delta p


Ed= (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


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