Question

# Consider a market that can be represented by a linear demand curve, QD = 200 –...

Consider a market that can be represented by a linear demand curve, QD = 200 – 2PD, (where QD is the quantity demanded and PD is the price that demanders pay) and a linear supply curve that QS = ½ PS (where QS is the quantity supplied and PS is the price that suppliers get).
a. What is the equilibrium price?
b. What is the equilibrium quantity?
c. What is demand elasticity at the equilibrium point?

1.) Let QD = Qs

PD = Ps = P .

Therefore,. QD=200-2P .......... (1)

And Qs = 1/2 P .........(2)

Solving (1) & (2) we get ,

200-2P = 1/2 P

Therefore , P= 80 , Which is the equilibrium price .

2) QD = 200-2PD

P= 80 ,

so , QD = 200-2*80 = 40 , which is the equilibrium quantity.

Supply function , Qs = 1/2*80 = 40.

3). Demand elasticity at equilibrium point is given by ,

P/Q * (∆Q /∆P)

QD = 200-2PD

Here , ∆Q/∆P = -2/1 = -2.

(Price , quantity) = (80,40)

Therefore elasticity at equilibrium point = (80/40)*-2 = -4.

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