Consider the demand curve q = 100-2p. Starting from an initial price of 10,
suppose the price increases by 5%. How much will the quantity demanded
change by (in percent)?
To find out how much the quantity demanded will change in response to a 5% increase in price, we can follow these steps:
Step 1: Given the initial price of 10, calculate the initial quantity demanded using the demand curve equation q = 100 - 2p.
q = 100 - 2(10) = 100 - 20 = 80
Step 2: Calculate the new price after a 5% increase:
New price = Initial price + (5% of Initial price)
= 10 + (0.05 * 10)
= 10 + 0.5
= 10.5
Step 3: Use the demand curve equation with the new price to calculate the new quantity demanded:
q_new = 100 - 2 * (10.5)
= 100 - 21
= 79
Step 4: Calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = [(Q_new - Q_initial) / Q_initial] * 100
= [(79 - 80) / 80] * 100
= (-1/80) * 100
= -1.25%
So, the quantity demanded will change by -1.25% in response to a 5% increase in price.