Why is it that a profit-maximizing businessman would never lower prices when facing an inelastic demand curve and might not lower price when facing an elastic demand curve?

Elastic demand is when the percentage change in quantity demanded is greater than the percentage change in price. In other words, when price changes, consumers' demand for the product changes significantly. On the other hand, inelastic demand is when the percentage change in quantity demanded is less than the percentage change in price. This means that when price changes, consumers' demand for the product does not change much.

A profit-maximizing businessman aims to earn the most significant profit possible. To do so, they need to find the optimal price for their product that will maximize the difference between their total revenue (price multiplied by quantity sold) and total costs.

When facing an inelastic demand curve, a price reduction will not significantly increase quantity demanded, resulting in a decrease in total revenue. Since costs remain constant or even increased due to higher production, the profit will decrease as a result. Therefore, it is not in the best interest of a profit-maximizing businessman to lower prices when facing an inelastic demand curve.

When facing an elastic demand curve, a price reduction can cause a significant increase in the quantity demanded. However, it is crucial to determine whether the increase in quantity demanded is enough to outweigh the decrease in price. In some cases, lowering the price might lead to a higher total revenue and, thus, increased profit. Nevertheless, in other situations, the price reduction might not be sufficient to increase revenue and profit. Consequently, a profit-maximizing businessman might not lower the price when facing an elastic demand curve if the potential increase in quantity demanded does not outweigh the price decrease. It is essential to analyze the specific situation and market conditions to make the optimal pricing decision.