Chapter 2, Problem 10CACQ

To determine

(a)

To explain:

The costs to the government in buying the unsold units of the firm.

Answer to Problem 10CACQ

The cost to the government in buying the firm’s unsold units is $480.

Explanation of Solution

Equilibrium price and quantity is calculated at a point where $Q_x^s=Q_x^d$

Substituting the values,

$\begin{array}{l}-16+P_x=92-2P_x\\ P_x+2P_x=92+16\\ 3P_x=108\\ P_x=\$36\end{array}$

Equilibrium price of the commodity is $36. At price of $36, equilibrium quantity demanded or supplied is calculated below:

$\begin{array}{l}{Q}_x^S=-16+P_x\\ =-16+36\\ =20\end{array}$

$\begin{array}{l}{Q}_x^d=92-2P_x\\ =92-2(36)\\ =92-72\\ =20\end{array}$

Therefore, at price $36, the quantity demanded and supplied is 20 units.

When government imposes price floor of $40 then the supplier likes to supply a higher quantity.

Calculate the quantity supplied at price floor $40:

$\begin{array}{l}{Q}_x^S=-16+P_x\\ =-16+40\\ =24\end{array}$

Calculate the quantity demanded at price floor $40:

$\begin{array}{l}{Q}_x^d=92-2P_x\\ =92-2(40)\\ =92-80\\ =12\end{array}$

It can be observed that the quantity supplied is greater than the quantity demanded.

Quantity demanded of the commodity decreases while quantity supplied by producers increases when government levied price floor. When government imposes price floor then producers want to produce more commodities while consumers demand less commodity as price of commodity is high.

The excess units supplied is 12 $\left(24-12\right)$

Calculate the cost of government buying firms:

$\begin{array}{c}\text{Cost}\text{of}\text{government}=\text{Excess}\text{units}\text{supplied×Price}\text{floor}\\ =12\times 40\\ =\$480\end{array}$

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

Economics Concept Introduction

Demand and supply:

Demand is the total quantity of goods that a consumer is ready and able to buy at various prices, keeping other things constant.Supply is the total quantity supplied by a producer at various prices, keeping other things constant.

Price floor:

Price floor is the maximum price set by the government below which goods are sold in an economy.When government imposes a price floor and agrees to purchase all units that consumer do not buy, it results in the cost to the government as government must purchase remaining unsold goods.

To determine

(b)

To explain:

The lost social welfare due to the price floor of $40.

Answer to Problem 10CACQ

The loss social welfare that stems from the $40 price floor is $456.

Explanation of Solution

The government is ready to purchase the difference between the quantity supplied and the quantity demanded in the market that is the surplus quantity in figure 1.

Due to price floor and government purchase, there are two types of dead weight loss. First due to higher price some consumer deterred which resulted into usual deadweight loss shown by area A.

Second, the excess produced goods are either destroyed or put in a warehouse and not consumed.

This deadweight loss is the loss of cost of production. The area given by the supply curve and this is the area under the supply curve and government purchases that is area B and C.

Thus, the summation of area A, B and C is the total dead weight loss.

$\text{DWL}=\text{Area}\text{of}\text{A}+\text{Area}\text{of}\text{B}+\text{Area}\text{of}\text{C}$

$\begin{array}{c}\text{DWL}=\text{Cost}\text{to}\text{the}\text{government}-\text{Area}\text{of}\text{D}\\ =\$480-\left(\frac{1}{2}\times \left(24-12\right)\times \left(40-36\right)\right)\\ =\$480-\left(\frac{1}{2}\times 12\times 4\right)\\ =\$480-\$24\\ =\$456\end{array}$

Therefore, the loss social welfare that stems from the $40 price floor is $456.

Economics Concept Introduction

Social welfare loss:

Social welfare loss refers to that amount which is usually caused to the whole society by imposition of tax by the government.