Final answer:
The price elasticity of demand can be calculated using the formula: Percentage Change in Quantity Demanded / Percentage Change in Price. When the price falls from 5 to 4, the price elasticity of demand is 1, indicating elastic demand. At q = 76, the price is 12.
Step-by-step explanation:
The price elasticity of demand can be calculated using the formula:
Price Elasticity of Demand = Percentage Change in Quantity Demanded / Percentage Change in Price
To calculate the percentage change in quantity demanded, we subtract the initial quantity from the final quantity and then divide by the initial quantity. Similarly, to calculate the percentage change in price, we subtract the initial price from the final price and then divide by the initial price.
Using the example given, when the price falls from 5 to 4, the percentage change in quantity demanded is:
(4 - 5) / 5 = -0.2 or -20%
And the percentage change in price is:
(4 - 5) / 5 = -0.2 or -20%
Now we substitute these values into the formula:
Price Elasticity of Demand = (-20% / -20%) = 1
Therefore, the price elasticity of demand as the price falls from 5 to 4 is 1. Since this value is greater than 1, it implies that the demand is elastic, meaning that a small change in price leads to a relatively larger change in quantity demanded.
For the second part of the question, we need the inverse demand function: p = 50 - 0.5q. Substituting q = 76 into the equation gives us:
p = 50 - 0.5(76) = 50 - 38 = 12
Therefore, at q = 76, the price is 12.