Question

2. (10 points) The demand of a product v depends on ts own price P). and the price of another product x (P.). The price elasticity of yvise-a.s, and ne cross-price elastiety with respect to X is o. (a) Are X and Y substitutes or complements? (b) Suppose now P, increases by 2%, and P" decreases by 5%. Will the quantity demanded of V increase or decrease? By what percent? 3. (20 points) The demand function of cigarettes is linear Q-1,50o-2 in packs, P is the price/pack in dollars. option (a) When P - $2, what is the elasticity of dema nd? Is the demand elastic or inelastic? (b) What is the price at which the demand for cigarettes has unitary elasticity s becomes (c) Suppose after an anti- cigarettes campaign, the demand function of soft drink -5000-20OP2, At the price you identified in (b), what is the elasticity of demand now given the new demand function? Is it elastic or inelastic?

Answer 1

Problem 2

Own price elasticity of demand=e_Y=-3.5

Cross price elasticity of demand of y with respect to x=e_YX=-0.8

a)

Cross price elasticity of demand of Y with respect to X is negative. It means if price of good x increases, demand of y will decrease and if price of good x decreases, demand of y will increase. We can say that X and Y are compliments.

b)

Percentage change in price of Y=dPy=+2%

Percentage change in price of X=dPx=-5%

Percentage change in quantity demanded of Y=(1+e_y*dpy)*(1+e_YXdPx)-1=(1-3.5*2%)*(1-0.8*(-5%))-1 =

-3.28%

Problem 3

Q=1500-250P

a)

Lets find Q at P=$2/pack

Q=1500-250*2=1000 packs

Given that Q=1500-250P

Differentiate Q with respect to P we get

dQ/dP=-250

Price elasticity of demand=(dQ/dP)*(P/Q)=-250*(2/1000)= -0.5

Absolute value of price elasticity is demand is less than 1, demand is inelastic at this point.

b)

Price elasticity of demand=(dQ/dP)*(P/Q)=-250*(P/Q)

Set Price elasticity of demand=-1 for unitary elastic demand

-250*(P/Q)=-1

Q=250P

Put Q=250P in demand function

Q=1500-250P

250P=1500-250P

P=(1500/500)=$3/pack

c)

Q=5000-200P^2

Lets find Q at P=3

Q=5000-200*3^2=3200

Differentiate Q with respect to P, we get

dQ/dP=-400P

Put P=3

dQ/dP=-400*3=-1200

Price elasticity of demand=(dQ/dP)*(P/Q)=-1200*(3/3200)= -1.125

Absolute value of price elasticity of demand is higher than 1, we can say that demand is elastic at this point