Chapter 5, Problem 3P

To determine

a.

The producer surplus, consumer surplus and total surplus in the absence of price floor.

Introduction: Consumer surplus refers to the additional profit a consumer gets due to the difference between the price of a commodity in the market and the price a consumer is ready to give for a particular commodity at a given period of time.

Producer surplus on the other hand is the additional surplus of the producers due to the difference in the price of a good at which the producer wants to the supply with the prices the consumers are ready to pay for a commodity in the market at a particular period of time.

Total surplus is the total sum of the consumer as well as the producer surplus in an economy in a given period of time. Total surplus is also referred to as the economic surplus.

Equilibrium price is the price of a commodity in the market at which both the consumers as well as the producers have no intension to change from.

Price floor refers to the minimum prices decided by the government of a country so as to minimize the change in the price of commodities.

Explanation of Solution

The diagram given below depicts the quantity demanded and quantity supplied of butter in billion pounds:

The consumer surplus in the absence of price floor in the market is calculated with the area below the demand curve and above the equilibrium prices in the economy. From the figure given above, the consumer surplus will be the area above the equilibrium price of $0.15 and below the equilibrium demand that is the area between quantities 0 to 200 billion.

Formula to calculate consumer surplus is as follows:

    $\text{Consumers}\text{surplus}=\frac{\left(\begin{array}{l}\left(\text{Price above equillibrium-Equillibrium price}\right)\\ \times \text{Equillibrium quantity demanded}\end{array}\right)}{2}$

Substitute, $0.25 for the price above equilibrium, 0.15 for equilibrium price and $200 for the equilibrium quantity demanded in the above formula,

    $\begin{array}{c}\text{Consumers}\text{surplus}=\frac{\left(\$0.25-\$0.15\right)\text{billion}\times 200\text{billion}}{2}\\ =\$10\text{billion}\end{array}$

Hence, consumer surplus is $10 billion.

Similarly, producer surplus can be calculated with the area above the supply curve but below the equilibrium prices.

Formula to calculate producer surplus is as follows:

    $\text{Producer}\text{surplus}=\frac{\left(\begin{array}{l}\left(\text{Equillibrium price-Price below equilibrium price}\right)\\ \text{×Equillibrium quantity demanded}\end{array}\right)}{2}$

Substitute 0.15 for the equilibrium price, 0.05 for the price below equilibrium price and $200 billion for equilibrium quantity demanded in the above formula,

    $\begin{array}{c}\text{Producer}\text{surplus}=\frac{\left(\$0.15-\$0.05\right)\text{billion}\times 200\text{billion}}{2}\\ =\$10\text{billion}\end{array}$

Hence, producer surplus is $10 billion.

Thus, formula to calculate total surplus is as follows:

$\text{Total Surplus}=\text{Consumer Surplus}+\text{Producer Surplus}$

Substitute $10 billion for consumer surplus and $10 billion for producer surplus in the formula.

    $\begin{array}{c}\text{Total}\text{surplus}=\$10+\$10\\ =\$20\text{ Billion}\end{array}$

Hence, the total surplus is $20 billion.

To determine

b.

Consumer surplus if price floor is at $0.18 and consumer buy 140 billion pounds of milk.

Explanation of Solution

If price floor is set at $0.18 per pound, the consumer will purchase at the prices above the price floor but below the maximum price level that is $0.25 as shown in the figure 1.

The formula to calculate consumer surplus as per this explanation is as follows:

    $\text{Consumer}\text{Surplus}=\left(\begin{array}{l}\left(\text{Maximum price-Floor Price}\right)\\ \text{×Equilbrium quantity}\end{array}\right)$

Substitute $0.25 for the maximum price, $0.18 for the floor price and 200 billion for the equilibrium quantity in the above formula,

    $\begin{array}{c}\text{Consumer}\text{Surplus}=\left(\$0.25-\$0.18\right)\times 200\text{ billion}\\ \text{=\$47}\text{billion}\end{array}$

Hence, the consumer surplus is $47 billion.

To determine

c.

The amount of producer surplus if price floor is at $0.18 per pound of milk and producers tend to sell 240 billion pounds of milk.

Explanation of Solution

With the price floor set, the producers tend to fix the sale of milk at 240 billion pounds. With this increased quantity more than the equilibrium quantity that was 1.65 billion.

Formula to calculate producer surplus is as follows:

    $\begin{array}{c}\text{Producer}\text{surplus}=\frac{\left(\text{Floor Price}-\text{Lowest price}\right)\times \text{sales}}{2}\\ \end{array}$

Substitute 0.18 for floor price, 0.05 for lowest price and 240 billion for sales in the formula.

    $\begin{array}{c}\text{Producer}\text{surplus}=\frac{\left(\$0.18-\$0.05\right)\times 240\text{billion}}{2}\\ =\frac{\$31.2}{2}\\ \text{=\$15}\text{.6}\text{billion}\end{array}$

Hence, the producer surplus is $15.6 billion.

To determine

d.

The money spent by the USDA (U.S. Department of Agriculture) to buy surplus milk.

Explanation of Solution

The USDA has to buy 240 million pounds of milk.

Formula to calculate the money spends to buy 240billion pounds of milk is as follows:

    $\text{Money}\text{spent}=\text{ Floor price}\times \text{Sale volume}$

Substitute, 0.18 for floor price and 240 billion for sales volume in the formula,

    $\begin{array}{c}\text{Money}\text{spent}=\$0.18\times 240\text{ billion}\\ =\$43.2\text{ Billion}\end{array}$

Hence, the amount of money spent is $43.2 billion.

To determine

e.

The total surplus in case of price floor and analyze the difference in the total surplus with price without a price floor.

Explanation of Solution

In case price floor is set by the government, the formula to calculate total surplus is as follows:

    $\text{Total}\text{surplus}=\text{Consumer}\text{surplus}+\text{Producer}\text{surplus}-\text{Money}\text{spent}$

Substitute, 47 Billion for consumer surplus, $15.6 Billion for producer surplus and $43.2 Billion for the money spent in the formula,

    $\begin{array}{c}\text{Total}\text{surplus}=\$47+\$15.6-\$43.2\\ =\$19.4\end{array}$

Hence, the total surplus is $19.4 billion.

The total surplus in an economy when price floor is set by the government is less as compared to the total surplus before the advent of price floor. This is because of the reduction in both the producer as well as the consumer surplus in the economy.