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I'm currently taking undergrad microeconomics and came across the following question:

The current price floor in the agricultural lettuce market makes it such that price of lettuce is 25% higher than equilibrium price and 100 heads of lettuce are demanded. Assuming that the elasticity of demand for lettuce is -0.50, what would be the equilibrium price and quantity of lettuce if the government removed the current price floor?

Here's how I've tried to solve the question: https://i.sstatic.net/2a4oY.jpg .

The answer is

Price = $0.75, Quantity = 112.5.

but I don't know how to solve that.

Thanks

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    $\begingroup$ you should add the attempt from that external site to your question in order to make it self contained. $\endgroup$
    – 1muflon1 ♦
    Commented Feb 8, 2021 at 22:28

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Price elasticity of demand of $-0.5$ means that if price increases by $1\%$ demand decreases by $0.5\%$ (and vice versa in case of decrease).

Consequently, if the equilibrium quantity with floor is $100$ and the price of lettuce is $25\%$ that means that eliminating the price flow - which will offset the $25\%$ will increase the quantity demanded by:

$$0.5\cdot25\% = 12.5\%$$

$12.5\%$ increase from $100$ is $112.5$ so that will be new quantity.

Regarding the price you don't mention what the price at the price floor originally was but it should decrease by $25\%$ from its original value.

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