Question

Consider a market where supply and demand are given by${\mathit{Q}}_{\mathbf{x}}^{\mathbf{s}}\mathbf{=}\mathbf{-}\mathbf{16}\mathbf{+}{\mathit{P}}_{\mathbf{x}}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}{\mathit{Q}}_{\mathbf{x}}^{\mathbf{d}}\mathbf{=}\mathbf{92}\mathbf{-}\mathbf{2}{\mathit{P}}_{\mathbf{x}}$.Suppose the government imposes a price floor of \(40, and agrees to purchase any and all units consumers do not buy at the floor price of $\mathbf{\backslash )}\mathbf{40}$per unit. a. Determine the cost to the government of buying firms’ unsold units. b. Compute the lost social welfare (deadweight loss) that stems from the$\mathbf{\$}\mathbf{40}$price floor.

Short answer

a)Quantity demanded is $12$units.

b) Dead weight loss is $\$456$units.

Step-by-step solution

Given Information:

$Q_x^s=-16+P_{x}and{Q}_x^d=92-2P_x$

Step 2:To find the quantity demand and dead weight loss:

Given the supply and demand functions are $Q_x^s=-16+P_{x}and{Q}_x^d=92-2P_x$.To determine the quality and demand supplied

$\begin{array}{rcl}{Q}_x^s& =& -16+P_x\\ & =& -16+40\\ Q_x^s& =& 24\end{array}$

Thus, the quantity supplied is $24$units

$\begin{array}{rcl}{Q}_x^d& =& 92-2P_x\\ & =& 92-2\times 40\\ & =& 92-80\\ Q_x^s& =& 12\end{array}$

Quantity demanded is $12$units

$\text{ExcessUnitsSupplied}=Q_x^s-Q_x^d$

Substitute the given equation$Q_x^d=12\text{and}{Q}_x^s=24$

$\begin{array}{rcl}CST& =& Q_x^s-Q_x^d\\ & =& 24-12\\ CST& =& 12\end{array}$

The excess units supplied is $12$units. To multiply the excess unit supplied to the amount of price floor

$12\times \$40=\$480$

The cost of buying firms unsold to the government is $\$480$units

To calculate the area of the triangle as

$\begin{array}{rcl}DWLArea& =& AreaA+AreaB+AreaC\\ & =& \frac{1}{2}\times (24-12)\times (40-36)\\ & =& \frac{1}{2}\times 12\times 4\\ & =& \frac{1}{2}\times 48\\ & =& 24\end{array}$

To subtract the cost to the government with the area of dead weight loss

$\$480-24=\$456$

Dead weight loss is $\$456$units.