Chapter 10, Problem 14E

To determine

(a)

To find:

The equilibrium price and quantity.

Answer to Problem 14E

The equilibrium price (P*) is $14 and quantity (Q*) is 15 units.

Explanation of Solution

Market equilibrium refers to a situation where the forces of demand and supply are balanced. Market equilibrium is achieved at an output level where quantity demanded is equal to quantity supplied. Given the demand and supply schedule, the equilibrium price (P) and quantity (Q) are (P*) $14 and (Q*) 15 units.

Economics Concept Introduction

Demand:

The quantity demanded of goods at different prices is referred as the demand for the goods. Demand curve is downward sloping.

Supply:

The quantity supplied of a good at different prices is referred as the supply of that good. Supply curve is upward sloping.

Market Equilibrium:

It refers to a situation where the forces of demand and supply are balanced.

To determine

(b)

To show:

The graphical representation of demand and supply curves.

Whether the demand and supply curves represent an individual firm's or market demand and supply curves, assuming market to be perfectly competitive. Also, explain the derivation of quantity supplied if the market is perfectly competitive.

Answer to Problem 14E

The graph of demand and supply curves is as shown below:

Figure (1)

The demand and supply curves given here are market demand and supply curves.

MC (Marginal Cost) is the supply curve and gives quantity supplied at each price for individual firm.

Explanation of Solution

In the Figure (1), the demand and supply curves and the equilibrium price and quantity are shown. Perfectly competitive market structure is one where there are large number of buyers and sellers. Other features of perfect competition are:

• Homogeneous products

• Industry is the price maker

• Firm is the price taker

• No individual buyer or seller can influence industry price

• Demand curve is AR curve which shows P=AR=MR.

Under perfect competition, individual firm's demand curve is the AR curve and since AR is constant for all levels of output, the demand curve is horizontal straight line. However, the market demand curve slopes downwards since it represents that industry output would be lower at a higher price and vice-versa.Therefore, the demand and supply curves given here are market demand and supply curves.

For a firm, quantity supplied is given by the MC curve. It is because, under perfect competition, at equilibrium, P=MR (=MC). Therefore, MC is the supply curvewhich gives quantity supplied at each price.

Economics Concept Introduction

Perfect competition:

It is a market structure where large number of buyers and sellers exist, and products are homogeneous.

Market demand:

Market demand for a good is the summation of all individual demands for that good.

Market supply:

Market supply is the summation of all individual supplies of that good.

Marginal Cost (MC):

The additional cost of producing an extra unit of output is referred to as the marginal cost of producing that unit of output.

To determine

(c)

To show:

The consumer and producer surplus.

Answer to Problem 14E

At P*=$14 and Q*=15 units, the consumer surplus is$45, and the producer surplus is $45.

Explanation of Solution

The consumer surplus and producer surplus are calculated below and shown graphically in the diagram below.

  $\begin{array}{c}\text{Consumer}\text{surplus}=\text{Area}\text{of}\text{the}\text{shaded}\text{triangle}\\ =\frac{1}{2}\times \left(20-14\right)\times \left(15-0\right)\\ =\frac{1}{2}\times 6\times 15\\ =\$45\end{array}$

  $\begin{array}{c}\text{Producer}\text{surplus}=\text{Area}\text{of}\text{the}\text{shaded}\text{triangle}\\ =\frac{1}{2}\times \left(14-8\right)\times \left(15-0\right)\\ =\frac{1}{2}\times 6\times 15\\ =\$45\end{array}$

Figure (2)

Economics Concept Introduction

Consumer surplus:

Consumer surplus is the difference between consumers' willingness to pay and the price that is charged to them. Graphically, it is the area between the demand curve and price line.

Producer surplus:

Producer surplus is the difference between the price producers receive and cost of production. Graphically, it is the area between the price line and the supply curve.

To determine

(d)

To explain:

The change in consumer and producer surplus as a result of a price ceiling of $12.Also, explain the change in consumer and producer surplus as a result of a price floor of $16.

Answer to Problem 14E

Change in consumer surplus after price ceiling is $15. That is, after price ceiling, consumer surplus increases by $15. The change in producer surplus after price ceiling is -$25. That is, after price ceiling, consumer surplus decreases by $25.

Change in consumer surplus after price floor is -$25. That is, after price floor, consumer surplus decreases by $25. The change in producer surplus after price floor is $15. That is, after price floor, producer surplus increases by $15.

Explanation of Solution

There is a price ceiling of $12 and equilibrium price is $14. Therefore, a price ceiling of $12 is binding. The effect of a price ceiling is shown in the diagram below. The new consumer and producer surplus with a price ceiling of $12 is calculated below.

  $\begin{array}{c}\text{Producer}\text{surplus}\text{(after}\text{price}\text{ceiling)}=\frac{1}{2}\times \left(12-8\right)\times \left(10-0\right)\\ =\frac{1}{2}\times 4\times 10\\ =\$20\end{array}$

  $\begin{array}{c}\text{Consumer}\text{surplus}\text{(after}\text{price}\text{ceiling)}=\left[\left(16-12\right)\times \left(10-0\right)\right]+\left[\frac{1}{2}\times \left(20-16\right)\times \left(10-0\right)\right]\\ =\left[4\times 10\right]+\left[\frac{1}{2}\times 4\times 10\right]\\ =40+20\\ =\$60\end{array}$

  $\begin{array}{c}\text{Change}\text{in}\text{producer}\text{surplus}\text{after}\text{price}\text{ceiling}=\$20-\$45\\ =-\$25\end{array}$

  $\begin{array}{c}\text{Change}\text{in}\text{consumer}\text{surplus}\text{after}\text{price}\text{ceiling}=\$60-\$45\\ =\$15\end{array}$

The diagram is as shown below:

Figure (3)

Change in consumer surplus after price ceiling is $15. That is, after price ceiling, consumer surplus increases by $15.

Change in producer surplus after price ceiling is -$25. That is, after price ceiling, consumer surplus decreases by $25.

A price floor is binding if it is above equilibrium price. The equilibrium price without floor is $14. Therefore, a price floor of $16 would be binding. The effect of a price ceiling is shown in the diagram below. The new consumer and producer surplus with a price ceiling of $12 is calculated below.

  $\begin{array}{c}\text{Consumer}\text{surplus}\text{(after}\text{price}\text{floor)}=\frac{1}{2}\times \left(20-16\right)\times \left(10-0\right)\\ =\frac{1}{2}\times 4\times 10\\ =\$20\end{array}$

  $\begin{array}{c}\text{Producer}\text{surplus}\text{(after}\text{price}\text{floor)}=\left[\left(16-12\right)\times \left(10-0\right)\right]+\left[\frac{1}{2}\times \left(12-8\right)\times \left(10-0\right)\right]\\ =\left[4\times 10\right]+\left[\frac{1}{2}\times 4\times 10\right]\\ =40+20\\ =\$60\end{array}$

  $\begin{array}{c}\text{Change}\text{in}\text{consumer}\text{surplus}\text{after}\text{price}\text{ceiling}=\$20-\$45\\ =-\$25\end{array}$

  $\begin{array}{c}\text{Change}\text{in}\text{producer}\text{surplus}\text{after}\text{price}\text{ceiling}=\$60-\$45\\ =\$15\end{array}$

Figure (4)

Change in consumer surplus after price ceiling is -$25. That is, after price ceiling, consumer surplus decreases by $25.Change in producer surplus after price ceiling is $15. That is, after price ceiling, producer surplus increases by $15.

Economics Concept Introduction

Consumer surplus:

Consumer surplus is the difference between consumers' willingness to pay and the price that is charged to them. Graphically, it is the area between the demand curve and price line.

Producer surplus:

Producer surplus is the difference between the price producers receive and cost of production. Graphically, it is the area between the price line and the supply curve.

Price ceiling:

A price ceiling is an upper limit for price which is generally imposed by the government.

Price floor:

A price floor is a lower limit for price which is generally imposed by the government.