Question

The demand for an economics textbook is given by: P = 250 –Q, where P is the price in dollars of a textbook and Q is the quantity demanded of textbooks (per week). Use the point price elasticityofdemandformulatocalculate: [Showyourworkinallpartsofthisquestion]

The price elasticity of demand at a price of $50 per textbook [3points]

The price elasticity of demand at a price of $150 per textbook [3points]

If the goal of the seller were to increase total sales revenue, would you recommend increasing the price of a textbook from $50 to $100? Briefly (in a sentence or two) explain your answer. [4 points]

Answer 1

P = 250 - Q

a)P

At P = 50,

Demand is Q = 200

Point elasticity of demand is given by e = (Q/P)*(P/Q)

Rewriting the demand function we have,

Q = 250 - P

Q/P = 1

Thus e = 1*50/200 = 0.25

b)

At P = 150,

Demand is Q = 100

Thus e = 1*150/100 = 1.5

c)

Total Revenue at P = 50: P*Q = 50*200 = 10000

Total Revenue at P = 150: P*Q = 150*100 = 150000

Hence the seller should increase the price.

When the elasticity of demand is less than one, a price increase raises the Total Revenue.