Question

In economics, the price elasticity of demand is the degree to which a proportional change in the price of a product causes a proportional drop in demand for the product. for instance, if elasticity is 0.5, that means that each 1% increase in price causes an approximately 0.5% decrease in quantity demand. when demand is linear with d(p)=b−ap , the price elasticity of demand, e(p) , at price p dollars per item is given by e(p)=apb−ap (a) we say that demand is inelastic at price p if e(p) is less than 1 . we say that demand is elastic at price p if e(p) is greater than 1 . let a=3 , b=120 . when p=10 , we have e(10)= 0.333 and therefore the demand is inelastic. . (b) it turns out that having demand that is neither elastic nor inelastic maximizes revenue from the sale of the product. if a=3 and b=120 , revenue is maximized when p= (c) as p increases without bound, e(p) will approach -1

Answer 1

Price elasticity of demand measures the sensitivity of demand to price changes. It's calculated by dividing the percentage change in quantity demanded by the percentage change in price. The elasticity can be categorized as elastic, inelastic, or unit elastic based on whether the value is greater than, less than, or equal to one.

Step-by-step explanation:

Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price. To compute this elasticity, we use the formula which divides the percentage change in quantity demanded by the percentage change in price. Goods with elastic demand have a high responsiveness to price changes with an elasticity greater than one. Conversely, goods with inelastic demand have a lower responsiveness to price changes, evidenced by an elasticity less than one.

For a linear demand equation like d(p) = b - ap, the price elasticity of demand e(p) at a given price p is calculated as e(p) = ap / (b - ap). When a=3 and b=120, at p=10, the calculation of e(10) shows that the demand is inelastic since it is less than one. To maximize revenue, firms often aim for a unitary elasticity where the percentage change in price and quantity demanded are equal.

As the price approaches infinity, or increases without bound, e(p) tends to approach -1. This is due to the fact that in the linear demand function, as p increases, ap becomes much larger than b - ap, causing the fraction to move toward zero, which indicates a highly inelastic demand at very high prices.