Question

Consider a market where supply and demand are given by QXS = −18

+ PX and QXd = 90 − 2PX. Suppose the government imposes a price
floor of $41, and agrees to purchase and discard any and all units
Consider a market where supply and demand are given by \( Q_{X}{ }^{S}=-18+P X \) and \( Q X^{d}=90-2 P X \). Suppose the government imposes a price floor of \( \$ 41 \), and agrees to purchase and di

Answer 1

With a price floor of $41 imposed by the government in a market where
`\( Q_X^(S) = -18 + P_X \)` and
`\( Q_X^(d) = 90 - 2P_X \)`, a surplus of 34 units will be created as the quantity supplied exceeds the quantity demanded at this price.

Step-by-step explanation:

To determine the impact of the $41 price floor in the given market, we set the quantity supplied
`(\( Q_X^(S) \))` equal to the quantity demanded
`(\( Q_X^(d) \))` at the imposed price.

Equating the supply and demand equations:

`\( Q_X^(S) = Q_X^(d) \)`

`\( -18 + P_X = 90 - 2P_X \)`

Solving for
`\( P_X \)`, we find the equilibrium price before the price floor:

`\( 3P_X = 108 \)`

`\( P_X = 36 \)`

At the price floor of $41, the quantity demanded can be found by substituting
`\( P_X = 41 \)` into the demand equation:

`\( Q_X^(d) = 90 - 2(41) = 90 - 82 = 8 \)`

Subtracting the quantity demanded from the quantity supplied at the price floor gives us the surplus:

`\( Q_X^(S) - Q_X^(d) = (-18 + 41) - 8 = 23 - 8 = 34 \)`

Hence, a surplus of 34 units will be created with the government agreeing to purchase and discard any excess units beyond the quantity demanded at the price floor of $41 in this market. This surplus represents the quantity supplied exceeding the quantity demanded due to the imposed price floor, leading to government intervention to manage the excess supply.

Complete Question:

Consider a market where supply and demand are given by
`\( Q_(X){ }^(S)=-18+P_X \)` and
`\( Q_X^(d)=90-2P_X \)`. Suppose the government imposes a price floor of $41 and agrees to purchase and discard any and all units exceeding the quantity demanded at this price. What is the impact of the price floor on the market, and what will be the resulting surplus or shortage?