1. Two points on a demand curve are P1=4, Q1=16 and P2=12, Q2=0. Find the equati

Question

1. Two points on a demand curve are P1=4, Q1=16 and P2=12, Q2=0.

Find the equation of the linear demand curve: Qd=a-bP

What is the price that will maximize revenue? What is the price elasticity of demand at this price?

2. Suppose the demand curve for bananas are given by the equation Qd=-250P+5000, the supply of bananas are given by Qs=600P+200.

Calculate the equilibrium price and equilibrium quantitiy.

If the new supply of bananas changes to Qd=600P. How does the new supply curve affect the new equilibrium price?

3. Consider the markets for widgets and cogs. You study survey data and observe that if widgets cost $5, the 100 widgets and 60 cogs are demanded. You also observe that if widgets cost $3, then 200 widgets are demanded and 150 cogs are demanded.

Calculate own-price elasticity of both goods.

Calculate cross-price elasticity of widgets with respect to cogs, are they substitutes? Are the compliments?

Explanation / Answer

1.

Two points on a demand curve are P1=4, Q1=16 and P2=12, Q2=0.

These 2 points must satisfy the equation of demand curve Q = a-bP

1st equation will be 16=a-4b

2nd equation will be 0=a-12b or a = 12b

solving these 2 equations

16 = 12b-4b

8b = 16 or b = 2

a=12*2 = 24

Q = 24-2P or 2P = 24-Q or P = 12-0.5Q

TR = P*Q = 12Q - 0.5Q^2

maximize TR, dTR/dQ = 12 - Q = 0

or Q = 12, the maximum revenue will be at Q = 12

P = 12-0.5*12 = 6

Price Elasticity of Demand

dQ/dP*P/Q = -2*(6/12) = -1

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