Question

Fill in blanks in the table below (with the given equation, marginal revenue is not stated nor given in the problem) for this demand equation ? = 10 − 1/2Q_d.

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

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

price?

Price (P)Quantity Demanded (Q)Total Revenue Price Elasticity of Demand 10 4 2

Answer 1

Quantity demanded is found using the demand function by placing the values of price in demand equation. This implies we have Qd = 20 - 2P. Total revenue is TR = PQ and price elasticity = ed = slope * P/Q or -2 x P/Q

1) Decrease in price causes revenue to increase till the demand is elastic (|ed| is > 1). This happens till a price of $5 beyond which the fall in price reduces total revenue as well

2) TR is maximum at a price of $5 and quantity of 10 units. Price elasticity is -1 at this level.

Price	Quantity demanded	Total revenue	Price elasticity of demand
10	0	0
9	2	18	-9.00
8	4	32	-4.00
7	6	42	-2.33
6	8	48	-1.50
5	10	50	-1.00
4	12	48	-0.67
3	14	42	-0.43
2	16	32	-0.25
1	18	18	-0.11