Question

. Elasticity and total revenue

Answer 1

The price elasticity of demand is the change in quantity demanded relative to the change in price.

• The second figure in the attached image represents the revenue graph
• The price elasticity of demand is 0.143
• The demand must be inelastic

Let:

$P \to Price\\Q \to Quantity$

(a) The total revenue

From the first graph (see attachment), we have:

$(P_1,Q_1) = (50,90)$

$(P_2,Q_2) = (75,81)$

$(P_3,Q_3) = (100,72)$

$(P_4,Q_4) = (125,63)$

$(P_5,Q_5) = (150,54)$

$(P_6,Q_6) = (175,45)$

$(P_7,Q_7) = (200,36)$

The total revenue (T) is calculated using:

$T = P \times Q$

So, we have:

$T_1 = 50 \times 90 = 4500$

$T_2 = 75 \times 81 = 6075$

$T_3 = 100 \times 72 = 7200$

$T_4 = 125 \times 63 = 7875$

$T_5 = 150 \times 54 = 8100$

$T_6 = 175 \times 45 = 7875$

$T_7 = 200 \times 36 = 7200$

The second figure in the attached image represents the revenue graph

(b) Price elasticity of demand

Between points A and B, we have:

$(P_1,Q_1) = (50,90)$

$(P_2,Q_2) = (25,99)$

The price elasticity of demand is:

$E_d = \frac{(Q_2 - Q_1)/(Q_1 + Q_2)/2}{(P_2 - P_1)/(P_1 + P_2)/2}$

So, we have:

$E_d = \frac{(Q_2 - Q_1)/(Q_1 + Q_2)}{(P_2 - P_1)/(P_1 + P_2)}$

$E_d = \frac{(99 - 90)/(90 + 99)}{(25 - 50)/(50 + 25)}$

$E_d = \frac{9/189}{-25/75}$

$E_d = -0.143$

The price elasticity of demand between points A and B is 0.143, and the demand must be inelastic because an increase in price of the bike leads to a decrease in the total revenue

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