Question

1. The demand for a slice of pizza in NYC is: Q_d = 10 - 4P

The supply of a slice of pizza in NYC is: Q_s = 3 + 3P

Refer to above information. If P = $2, is there a surplus or shortage? What is the size of the surplus or shortage? (6 pts)

2. Consider the demand curve Q_D = 6 – 3P and the supply curve Q_S = P + 5. What is the price elasticity of demand at market equilibrium? (9 pts)

Answer 1

1)

At P = $2,

Q_D = 10 - 4(2)

= 2

Q_s = 3 + 3 (2)

= 9

So, at price equal to $2, there is a surplus in the market, i.e, supply is greater than demand.

Surplus = 7 units

2)

Q_D = 6 – 3P

Q_S = P + 5

At equilibrium, Q_D = Q_S

6 - 3P = P + 5

1 = 4P

P = $0.25

Q = 6 - 3(0.25)

Q = 5.25

(d/dP) Q_D = -3

Price elasticity of demand = (change in Q / change in p) * (P/Q)

= -3 * ( 0.25 / 5.25)

= - 0.142, where the negative sign indicates the inverse relationship between price and quantity demanded.