Question

. Fill in blanks in the table below for this demand equation ? = 10 − 1 2 ?? .

Answer the following questions based on your answer in the table above:

a. Does a decrease in price necessarily increase total revenue?

b. For what price the total revenue is maximum? What is the price elasticity of demand for that price?

Price (P)	Quantity Demanded (QD)	Total Revenue	Price Elasticity of Demand Price
10
9
8
7
6
5
4
3
2
1

Answer 1

P	Q	TR	Elasticity
10	0.03	0.3	-26.67
9	0.11	0.99	-6.54
8	0.19	1.52	- 3.37
7	0.27	1.89	- 2.07
6	0.35	2.1	- 1.37
5	0.43	2.15	- 0.93
4	0.51	2.04	- 0.63
3	0.59	1.77	- 0.41
2	0.67	1.34	- 0.24
1	0.75	0.75	- 0.11

P = 10 -12Q

12Q = 10 - P

Q = 0.83 - 0.08P

delta Q / delta P = - 0.08

Following formulas are used:

Elasticity at P and Q = (delta Q / delta P)*(P/Q)

Total Revenue = P*Q

a. Does a decrease in price necessarily increase total revenue?

No. It depends upon the price and quantity effect both. We see in the table that TR increases only till P = 5. After this price, it falls

b. For what price the total revenue is maximum? What is the price elasticity of demand for that price?

For P = 5, TR is maximum = 2.15. The corresponding absolute elasitcity = 0.93 (close to unit)

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