Suppose you have the generic demand curve Q 3000 400P 300

Suppose you have the generic demand curve

Q = 3000 - 400P – 300P1 + 200P2 + 0.05I

Where P is the price of the good, P1 and P2 are prices of related goods and I is income.

Currently P is $1.00, P1 is $0.50, P2 is $1.50 and I is $50,000.

1)Calculate demand using the current market conditions. 2)Is P1 a substitute or complement? (Why) 3) Is P2 a substitute or complement? (Why) 4) Is this product normal it inferior to Income? (Why) 5) Under current market conditions calculate the price elasticity for this product. 6) What conclusions can be made from the elasticity you calculated in question 5?

Solution

A.

Q = 3000 - 400P – 300P1 + 200P2 + 0.05I

Current market condition:

P is $1.00, P1 is $0.50, P2 is $1.50 and I is $50,000. Putting the value in demand curve

Q=3000-400*1-300*.5+200*1.5+.05*50000

=5250

b.

dQ/dP1 is negative which means with increase of price of good 1, quantity of good demanded decreases. So good and 1 complement.

c.

Cross price elasticity of good 2 is positive (as dQ/dP2>0). Therefore, they are substitute.

d.

Income elasticity is greater than zero. So with increase in income quantity demanded of good increases. So good is normal.

e.

dQ/dP=-400

Q=5250, P=1

Elasticity=dQ*P/Q*dP=-400/5250=-.076

f.

Elasticity is less than 1,therefore demand curve is inelastic in current market scenario. With rise in price, quantity will not fall proportionately.