1. JQ sells ties and currently has sales of 1,200 units a month, producing a revenue of £36,000. It competes with KR, who is now considering a price cut of 25%. The PED for JQ is –1.5 and the CED between the two products is 0.8.

a) Calculate the effect of KR’s price cut on the sales volume and revenue of JQ.

b) Assuming KR does cut its price by 25%, determine the price that JQ would have to charge to restore its sales volume to its previous level.

c) Calculate the effects of the decisions in a) and b) above on profit compared with the original profit, assuming that JQ’s ties cost £20 to produce. Is JQ’s retaliatory price cut a good decision?

a) To calculate the effect of KR's price cut on the sales volume and revenue of JQ, we need to consider the price elasticity of demand (PED) for JQ's ties. The formula for calculating the percentage change in quantity demanded is:

Percentage change in quantity demanded = PED * Percentage change in price

Given that PED for JQ is -1.5 and KR is considering a price cut of 25%:

Percentage change in quantity demanded = -1.5 * (-25%) = 37.5%

The percentage change in quantity demanded represents the change in sales volume. Therefore, JQ's sales volume will decrease by 37.5% due to KR's price cut.

To calculate the change in revenue, we multiply the percentage change in quantity demanded by the original revenue:

Change in revenue = 37.5% * £36,000 = £13,500

JQ's revenue will decrease by £13,500 due to KR's price cut.

b) To determine the price that JQ would have to charge to restore its sales volume to its previous level, we need to calculate the percentage change in price required. Using the same formula as above:

Percentage change in price = (Percentage change in quantity demanded) / PED

Percentage change in price = (37.5%) / (-1.5) = -25%

The negative sign in the percentage change in price indicates that JQ needs to decrease its price to restore its sales volume. Therefore, JQ would have to cut its price by 25% to maintain its previous sales volume.

c) To calculate the effects of the decisions on profit, we need to consider the cost of producing JQ's ties. Given that the cost is £20 per tie, the original profit can be calculated as:

Original profit = (Revenue - Cost) * Sales volume
Original profit = (£36,000 - £20) * 1,200 = £43,920

Effect on profit from KR's price cut:
The change in profit can be calculated by multiplying the change in revenue by the profit margin (revenue per unit minus cost per unit):

Change in profit = Change in revenue * (Revenue per unit - Cost per unit)
Change in profit = £13,500 * (£36,000 / 1,200 - £20) = £13,500

Effect on profit from JQ's retaliatory price cut:
The change in profit can be calculated in the same way:

Change in profit = Change in revenue * (Revenue per unit - Cost per unit)
Change in profit = (£36,000 * (1 - 0.25) - £20) * (1,200 / 0.8) - (£36,000 - £20) * 1,200 = -£6,000

Comparing the effects on profit, the change caused by KR's price cut is an increase of £13,500, while JQ's retaliatory price cut results in a decrease of £6,000. Therefore, JQ's retaliatory price cut is not a good decision in terms of profit.