Assume a firm sells 1m units of its product for $10 and has a 30% gross profit margin ($3). cutting the price to $9.50 might stimulate unit sales by 10%. will the assumed increase in sales volume offset the decrease in margin?

Case 1: Unit price = $10

Profit = $3 * 1m = $3m

Case 2: Unit price = $9.50

Since cost per unit is constant which is $7, therefore profit per unit is now $2.50.

Profit = $2.50 * 1m * 1.10 = $2.75m

Therefore the increase in sales volume does not offset the decrease in profit margin.