Final answer:
To break even on a 10% discount, approximately an 11.11% increase in sales volume is needed. Another 10% discount on a product may not result in a uniform 8% increase in quantity demanded due to various market factors. Changes in interest rates affect bond valuations inversely, while wage increase percentages are calculated by dividing the increase by the original wage.
Step-by-step explanation:
To answer the question of what increase in volume is needed to break even on a 10% discount, we need to consider the concept of price elasticity of demand, which is a measure used to show the responsiveness of the quantity demanded of a good or service to a change in its price.
It's not as straightforward as logarithmic dilution mentioned in the reference, which applies to the concentration changes in solutions in chemistry. Instead, this involves understanding that revenue is the product of price and quantity.
A 10% discount will decrease revenue per unit, so to maintain the same overall revenue, the quantity sold must increase. The percentage increase in quantity needed to offset a 10% price reduction is calculated by the equation 1/(1 - discount rate). So for a 10% discount, the calculation is 1/(1 - 0.10) = 1.1111, meaning an increase in sales volume of approximately 11.11% is needed to break even.
If a previous 10% decrease in price resulted in an 8% increase in quantity demanded, another 10% decrease may not necessarily lead to an additional uniform increase due to factors such as market saturation, consumer preferences, or the product's price elasticity not remaining constant. In the bond market, changes in interest rates inversely affect bond prices; if interest rates rise, existing bonds with lower rates become less valuable, so you would pay less than the face value (e.g., less than $10,000). Conversely, if interest rates decrease, the bond's value would increase since it offers a relatively higher return.
Similarly, when discussing wage increases, if you receive a $2 per hour raise on a $10 per hour wage, your percentage increase in pay is 20%. Therefore, a percentage change in quantity demanded or a wage can be calculated by dividing the change by the original amount and converting it to a percentage.