Question

The market demand for a hamburger is given by the equation Qd=6-0.5P

1. Derive the market demand schedule and the toral revenue if the price per hamburger takes the following values: $12, $10, $6, $6, $4, $2, $0.
2. Using this information about demand and the total revenue, draw the demand and TR revenue curves.
3. Use the point elasticity formula, compute the price elasticity of demand at each hamburger price and show the relationship between the price elasticity of demand and the total revenue for each price on the demand curve you have drawn.   

Answer 1

a.

P	Mkt Demand	TR
12	0	0
10	1	10
6	3	18
6	3	18
4	4	16
2	5	10
0	6	0

b.

c.

Elasticity between p1 = 12 and P2 = 10

Q1 = 0 and Q2 = 1

Elasticity of Demand = [(Q2 - Q1) / (Q2+Q1)/2] / [(P2 - P1) / (P2+P1)/2]

= [(1 - 0) / (1+0)/2] / [(10 - 12) / (10+12)/2]

= -2/0.18

= -11.11

Elasticity between p1 = 10 and P2 = 6

Q1 = 1 and Q2 = 3

Elasticity of Demand = [(Q2 - Q1) / (Q2+Q1)/2] / [(P2 - P1) / (P2+P1)/2]

= [(3 - 1) / (3+1)/2] / [(6 - 10) / (6+10)/2]

= -1/0.5

= -2

Elasticity between p1 = 6 and P2 = 6

Q1 = 3 and Q2 = 3

Elasticity of Demand = [(Q2 - Q1) / (Q2+Q1)/2] / [(P2 - P1) / (P2+P1)/2]

= [(3 - 3) / (3+3)/2] / [(6 - 6) / (6+6)/2]

= 0

Elasticity between p1 = 6 and P2 = 4

Q1 = 3 and Q2 = 4

Elasticity of Demand = [(Q2 - Q1) / (Q2+Q1)/2] / [(P2 - P1) / (P2+P1)/2]

= [(4 - 3) / (4+3)/2] / [(4 - 6) / (4+6)/2]

= -0.2857/0.4

= -0.71

Elasticity between p1 = 4 and P2 = 2

Q1 = 4 and Q2 = 5

Elasticity of Demand = [(Q2 - Q1) / (Q2+Q1)/2] / [(P2 - P1) / (P2+P1)/2]

= [(5 - 4) / (5+4)/2] / [(2 - 4) / (2+4)/2]

= -0.22/0.66

= -0.33

Elasticity between p1 = 2 and P2 = 0

Q1 = 5 and Q2 = 6

Elasticity of Demand = [(Q2 - Q1) / (Q2+Q1)/2] / [(P2 - P1) / (P2+P1)/2]

= [(6 - 5) / (6+5)/2] / [(0 - 2) / (0+2)/2]

= -0.18/2

= -0.09

So, we observed that as TR increases initially, the demand is elastic. Demand becomes inelastic when TR starts falling