Question

Suppose demand and supply are given by ${\mathbf{Q}}^{\mathbf{d}}\mathbf{=}\mathbf{60}\mathbf{-}\mathbf{P}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{Q}}^{\mathbf{s}}\mathbf{=}\mathbf{P}\mathbf{-}\mathbf{20}$.

a. What are the equilibrium quantity and price in this market?

b. Determine the quantity demanded, the quantity supplied, and the magnitude of the surplus if a price floor of $\mathbf{\backslash (}\mathbf{50}$is imposed in this market.

c. Determine the quantity demanded, the quantity supplied, and the magnitude of the shortage if a price ceiling of $\mathbf{\backslash )}\mathbf{32}$is imposed in this market. Also, determine the full economic price paid by consumers.

Short answer

1. Equilibrium quantity in this market is$20\mathrm{units}$
2. The magnitude of surplus is imposed in the market is$100\mathrm{units}$.
3. The Full Economic price paid by customers are$\mathrm{\$}48$ units

Step-by-step solution

Given Information:

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{d}}=60-\mathrm{P}\\ {\mathrm{Q}}^{\mathrm{s}}=\mathrm{P}-20\end{array}$

Price floor =$\mathrm{\$}50$ ,

Price ceiling =$\mathrm{\$}32$

Finding the equilibrium quantity and price in the market

a.

Equilibrium price and quantity are identified equalizing supply and demand.

${\mathrm{Q}}^{\mathrm{d}}={\mathrm{Q}}^{\mathrm{s}}$

Substituting the given data values in this equation,

$\begin{array}{c}60-\mathrm{P}=\mathrm{P}-20\\ 2\mathrm{P}=80\\ \mathrm{P}=40\end{array}$

Thus, the equilibrium price in market is$\mathrm{P}=\mathrm{\$}40$

For demand function as

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{d}}=60-\mathrm{P}\\ =60-40\\ =20\end{array}$

Thus, the equilibrium price in market is 20 units

Finding the equilibrium quantity and price when price floor level is P=$50

b.

Demand function as

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{d}}=60-\mathrm{P}\\ =60-50\\ =10\end{array}$

Supply function as

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{s}}=\mathrm{P}-20\\ =50-20\\ =30\end{array}$

To find the shortage as

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{s}}-{\mathrm{Q}}^{\mathrm{d}}\\ =30-10\\ =20\end{array}$

The magnitude of surplus is imposed in the market is

$\begin{array}{l}\mathrm{P}\times {\mathrm{Q}}^{\mathrm{s}}-{\mathrm{Q}}^{\mathrm{d}}\\ =50\times 20\\ =1000\end{array}$

Finding the equilibrium quantity and price when price ceiling level is P=$32

c.

Demand function as

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{d}}=60-\mathrm{P}\\ =60-32\\ =28\end{array}$

Supply function as

$\begin{array}{c}{\mathrm{Q}}^{\mathrm{s}}=\mathrm{P}-20\\ =32-20\\ =12\end{array}$

To find the shortage as

$\begin{array}{c}\mathrm{Shortage}={\mathrm{Q}}_{\mathrm{d}}-{\mathrm{Q}}_{\mathrm{s}}\\ =28-12\\ =16\end{array}$

Thus,

$\begin{array}{c}\mathrm{Shortage}=32\times 16\\ =512\end{array}$

${\mathrm{P}}^{\mathrm{C}}=32\mathrm{and}{\mathrm{P}}^{\mathrm{F}}=48$

The full economic price in this equation as

$\begin{array}{c}{\mathrm{P}}^{\mathrm{F}}={\mathrm{P}}^{\mathrm{C}}+({\mathrm{P}}^{\mathrm{F}}-{\mathrm{P}}^{\mathrm{C}})\\ =32+(48-32)\\ =32+26\\ =58\end{array}$

Thus, the full economic price paid by customers is $58.