Final answer:
The price elasticity of demand is calculated using the formula E = (% change in quantity demanded) / (% change in price). For the given scenarios, the price elasticities of demand are -2 and -1, indicating different levels of elasticity and inelasticity. The price elasticities of demand can vary depending on the price range.
Step-by-step explanation:
To calculate the price elasticity of demand, we need to use the formula:
E = (% change in quantity demanded) / (% change in price)
For the first scenario:
% change in quantity demanded = [(4 - 5) / ((4+5)/2)] x 100 = -22.22%
% change in price = [(5 - 4) / ((5+4)/2)] x 100 = 11.11%
Using these values, we can calculate the price elasticity of demand:
E = (-22.22%) / (11.11%) = -2
For the second scenario:
% change in quantity demanded = [(8 - 9) / ((8+9)/2)] x 100 = -11.11%
% change in price = [(9 - 8) / ((9+8)/2)] x 100 = 11.11%
Using these values, we can calculate the price elasticity of demand:
E = (-11.11%) / (11.11%) = -1
Would you expect these answers to be the same?
No, these answers would not be the same because the price elasticities of demand for different price ranges can vary. In this case, the first scenario (-2) indicates that the demand is relatively elastic, meaning a small change in price leads to a larger change in quantity demanded. The second scenario (-1) indicates that the demand is relatively inelastic, meaning a change in price has a smaller effect on the quantity demanded.