Question

1. The graph below illustrates the two markets (D1 where Q1 = 8 -0.5P and D2 where Q2 = 20 – 2P) that a single firm is currently serving: N NA OD ON A 0 0 0 D2 10 12 14 16 18 20 Quantity a) For any exact same change in price, which market (D1 or D2) is more elastic? (You must motivate your answer based on class concepts) b) Assuming that the firm is current charging a price of $8/unit in both markets, determine if the point elasticity elastic or inelastic in each market. c) If the firm wants to maximize revenue, what price should they be charging in each market? (Motivate) d) If the point price elasticity of demand in a market has the absolute value of two (2) and prices decreases by 10%, how much will the quantity demanded change?

Answer 1

a) D2 is more elastic as its shows that a little change in price changed a lot in quantity demanded.

b) Current price = $8

Point elasticity of demand = Lower segment / Upper segment

As per pythagorus theorem = Base² + Height² = Hypotenuse² in a right angle triangle.

For D1:

Point elasticity of demand = AH / HF

AH² = AC² + CH² = 64 + 16 = 80

AH = 8.94

HF² = HE² + EF² = 64 + 16 = 80

HF = 8.94

Point elasticity of demand = AH / HF = 8.94 / 8.94 = 1

Unitary elastic when price = $8.

For D2:

Point elasticity of demand = BH / HG

BH² = BC² + CH² = 4 + 16 = 20

BH = 4.47

HG² = HE² + EG² = 64 + 256 = 320

HG = 17.88

Point elasticity of demand = BH / HG = 17.88 / 4.47 = 4

Elastic demand when price = $8 as Elasticity of demand > 1

Priie & ce -- by buy get to the

c) If firm wants to maximize profit, total revenue should be maximum:

D1 = 8 - 0.5P

Total revenue = Price * Quantity

Total revenue = 8P - 0.5P²

Marginal revenue = 8 - P

To maximum Total revenue, marginal revenue should be zero.

8 - P = 0

P = 8

They should charge $8 to maximize profit.

D2 = 20 - 2P

Total revenue = Price * Quantity

Total revenue = 20P - 2P²

Marginal revenue = 20 - 4P

To maximum Total revenue, marginal revenue should be zero.

20 - 4P = 0

P = 5

They should charge $5 to maximize profit.

d) Point elasticity of demand = 2

%change in price = 10%

Price elasticity of demand = %change in quantity demanded / %change in price

2 = %change in quantity demanded / 10%

%change in quantity demanded = 20%

If price falls by 10%, quantity demanded will rise by 20%.