Suppose the demand and supply curves for a computer software

Suppose the demand and supply curves for a computer software are as follows:

Q_d = 189 - 2.25P

Q_s = 124 + 1.5P

The price is measured in dollars. Equilibrium is $1.59

1. At the market equilibrium, what is the price elasticity of demand?

2. If the government regulates the price to be $15, what will happy to the market? Surplus or shortage? How much?

Solution

Elasticity of demand = - (dQ/dP)*(P/Q) = -(-2.25)*(1.59/185.4425)

at P=1.59 Q = 185.4425 =0.019294

If the government regulates the price at $15 then there will be excess supply in the market because the price set is above the equilibrium price and the consumers will not demand it. But the producers will supply more to earn greater revenues.

At P = 15 Qd =189-2.25*15 = 155.25

Qs=124+1.5*15 = 146.5

Excess = 155.25 - 146.5 = 8.75