If P=100-2Q, and p=2Q, how do you find the surplus of units? Suppose that the inverse demand equation is p=100-2Q, and the supply equation is p=20

Economics Dec 13, 2020

If P=100-2Q, and p=2Q, how do you find the surplus of units? Suppose that the inverse demand equation is p=100-2Q, and the supply equation is p=20. If the price is controlled at $55, this is a price floor. In this market. there will be a surplus of how many units (enter your response as a real number rounded to one decimal place)?

Expert Solution

We first compute the quantity without the price floor, i.e., the equilibrium price. At the equilibrium price, quantity demanded is equal to quantity supplied, i.e.,

100 - 2Q = 2Q
4Q = 100
Q = 25

and the equilibrium price is P = 2 * 25 = $50.

When there is a price floor of $55, which is above the equilibrium price, then the floor will be binding. At the price floor, the quantity demanded is max(0, 100 - 2 * 55) = 0. The quantity supplied is 2 * 55 = 110. So the surplus is 110 - 0 = 110.

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