Hi Everyone, I got the below from a casebook. The way I solved it was to use an assumption for volume, say volume = 100 units. Is there a more elegant way to do so though?

One option that our client has is to give in to its customers’ demands for a price discount. However our client is concerned about the impact this will have on its profits. If we were to cut prices 5%, how much would we have to increase volumes to maintain the same amount of profits?

In this case the gross margin is 20%. So if the original price is 100, then per unit costs are 80 and profits 20. A 5% decline in price makes it 95. Costs remain at 80 and profits are now 15. To make the profits the same, you need to increase volume by one third. So cutting prices to take back market share, requires that it sell 33.3% more product simply to keep profits constant. Given its high market share levels, this is unlikely.