The quantity of TVs sold is 100 at the unit price $200. Suppose the price elasticity of demand for TVs by the initial value method is 2.0, and you would like to decrease the unit price for TVs to $150. Then the new quantity sold must be __________ .
A. 125
B. 150
C. 200
D. 250
I think its B; can someone help me?
oops It's D 250
To find the new quantity sold, we'll use the price elasticity of demand formula:
Elasticity = percentage change in quantity demanded / percentage change in price
Given that the price elasticity of demand is 2.0, we can rewrite the formula as:
2.0 = percentage change in quantity demanded / percentage change in price
We know the initial quantity sold is 100, and the initial unit price is $200. We want to decrease the unit price to $150 and find the new quantity sold.
Percentage change in price = (new price - initial price) / initial price = ($150 - $200) / $200 = -0.25
Now, solving for the percentage change in quantity demanded:
2.0 = percentage change in quantity demanded / -0.25
Cross-multiplying, we get:
percentage change in quantity demanded = 2.0 * -0.25 = -0.5
To find the new quantity sold, we'll use the formula:
New quantity sold = initial quantity sold * (1 + percentage change in quantity demanded)
Substituting the values:
New quantity sold = 100 * (1 + (-0.5)) = 100 * 0.5 = 50
Therefore, the new quantity sold is 50. None of the options provided match this result, so it seems there may be an error in the given options.