Question

9.   Find the equations for Demand and Supply, and determine the market equilibrium price and quantity. (P is the y variable, and the QS and QD are x variables).

•   Demand equation: P = _______________________

•   Supply equation: P = ________________________

•   Market equilibrium price: ______________

•   Market equilibrium quantity: ___________
P    QS   QD
400   1600   3000
450   1800   2500
500   2000   2000
550   2200   1500
600   2400   1000

•   Find the numerical value of price elasticity of demand where P = 600.

Answer 1

When P = 400 , Q_D = 3000

When P = 450, Q_D = 2500

Slope of the demand curve = -(50/500) = - 0.1

Let Y be the intercept of the Demand curve on the y axis.

Inverse demand function is

P = Y - 0.1Q_D

When, P = 400, Q_D = 3000

400 = Y - 0.1*3000

400 = Y - 300

Y = 700

1. Thus, the demand function is P = 700 - 0.1Q_D

Or, Q_D = 7000 - 10P

Similarly we can determine the supply function

P = X + 0.25Q_S

When, P = 400, Qs = 1600

400 = X + 0.25*1600

X = 0

2. Supply function is P = 0.25Q_S

Or, Q_S = 4P

Now equate Q_D with Qs

7000 - 10P = 4P

14P = 7000

P* = 500

Q* = 2000

3. Equilibrium price: P* = $ 500 per unit

4. Market Equilibrium Quantity: Q* = 2000 units

Elasticity can be calculated using the following formula

Differentiating the demand function wrt P we get

At P = 600, Q = 1000

Elasticity of demand (at P = 600) = - 6

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