Question

suppose the demand curve for a product is given by Q=10-2P+Ps1,where P is the price of the product and Ps is the price of a substitute good. the price of the substitute good is $2.00.

a)suppose P=$1.00, what is the price elasticity of demand?what is the cross- price elasticity of demand?

b)suppose the price of the good, P, increases to $2.00. Now what is the price elasticity of demand, and what is the cross-prices elasticity of demand?

Answer 1

The demand curve for a product is given by Q = 10 - 2P + Ps.

P is the product's price, and 'Ps' is the price of a substitute good. The price of substitute goods is $2.

Now demand curve is Q = 10 - 2P + 2

Q = 12 - 2P...............................(1)

(a) Suppose the price of good 'P' is given equally to $1, then demand would be Q = 12 - 2*1

Q = 10 units

Price elasticity of demand = \DeltaQ/\DeltaP * P/Q

\DeltaQ/\DeltaP is the slope of the demand curve. We can calculate the slope from the demand curve. The first derivative of the demand curve will be the slope of the demand curve.

Q = 10 - 2P + Ps

\DeltaQ/\DeltaP = - 2

Therefore, the price elasticity of demand is Ed = -2 * 1/10

Ed = 0.2 is the price elasticity of demand.

For cross-price elasticity, we will differentiate the demand curve concerning the price of substitute goods.

Q = 10 - 2P + Ps

\DeltaQ/\DeltaPs = 1

Cross price elasticity = \DeltaQ/\DeltaPs * Ps/Q

Cross price elasticity = 1 * 2/10

Cross price elasticity = 0.2

(b) Suppose the good's price is 'P' = $2 and Ps is constant at $2. The slope of the demand curve will remain the same as before. Demand will be,

Q = 10 - 2*2 + 2

Q = 8 units

Now price elasticity = - 2 * 2/8

Ed = 0.5 this price elasticity.

Cross price elasticity = 1 * 2/8

Cross price elasticity = 0.25