Chapter 9, Problem 9.7P

a.

To determine

The equilibrium price, consumer surplus, and producer surplus in the equilibrium.

Answer to Problem 9.7P

The equilibrium price is $400, producer surplus is $20,000 and consumer surplus is $16,000.

Explanation of Solution

The demand for the broccoli is given by,

  $Q^d=1,000-5P$ , and supply is as follows,

  $Q^s=4P-80$ ,

Equilibrium is a point where the demand and supply curve meet. Hence this point will be,

  $Q^s=Q^d$

  $4P-80=1,000-5P$

  $P=\$120$ ,

Hence the equilibrium price is $120. Now substitute this value in above equation, we get,

  $Q^s=4P-80$ ,

  $Q=4\times 120-80$

  $Q=480-80$

  $Q=400$

Hence the equilibrium quantity is 400 units. Now the total expenditure is calculated as follows,

  $E=P\times Q$ ,

  $=400\times 120$ ,

  $=\$48,000$

Now the consumer surplus is calculated by as follows,

  $Consumer\text{ surplus=}\frac{1}{2}\times Base\times Height$ ,

  $=\frac{1}{2}\times Q\times (P_m-P^{*})$

  $=0.5(200-120)(400)$

  $=\$16,000$

Hence the consumer surplus is $16,000.

Now the producer surplus is calculated below,

  $\mathrm{Pr}oducer\text{ surplus=}\frac{1}{2}\times Base\times Height$ ,

  $=\frac{1}{2}\times Q\times (P^{*}-P_s)$

  $=0.5(120-20)(400)$

  $=\$20,000$

Hence, the producer surplus is $20,000.

Economics Concept Introduction

Introduction:Consumer surplus is a difference between the amount which consumer actually pays and the amount which he is willing to pay.

Producer surplus is the difference between what the consumer is willing to accept for a given quantity of money or good and the how much a person actually receives by selling the good in the market at the prevailing prices.

b

To determine

To describe: The total loss in consumer surplus and producer surplus, provided some values are changed.

Answer to Problem 9.7P

Hence the new consumer surplus is $12,000 and new producer surplus is $15,000.

Explanation of Solution

Suppose Q= 300, the total consumer surplus is calculated as follows,

  $Consumer\text{ surplus=}\frac{1}{2}\times Base\times Height$ ,

  $=\frac{1}{2}\times Q^{*}\times (P_m-P^{*})$

  $=0.5(200-120)(300)$

= $=\$12,000$

Thus the new consumer surplus is $12,000 and it is decreased by the amount of $4,000. Now the producer surplus is calculated by as follows,

  $\text{Producer surplus=}\frac{1}{2}\times Base\times Height$ ,

  $=\frac{1}{2}\times Q\times (P^{*}-P_s)$

  $=0.5(120-20)(300)$

  $=\$15,000$

Thus the new producer surplus is $15,000 and it is decreased by the amount of $5,000.

Economics Concept Introduction

Introduction: Consumer surplus is a difference between the amount which consumer actually pays and the amount which he is willing to pay.

Producer surplus is the difference between what the consumer is willing to accept for a given quantity of money or good and the how much a person actually receives by selling the good in the market at the prevailing prices.

c.

To determine

To describe: The allocation of producer and consumer surplus between suppliers and demanders are dependent upon the price at which broccoli is sold.

Answer to Problem 9.7P

As the equilibrium price increases, consumer surplus will decreased by $7,000 and producer surplus will increased by $8,800. If price will be $95 then producer surplus is decreased by $8,750 and consumer surplus is decreased by $11,562.50.

Explanation of Solution

Let the equilibrium price P = $140, then consumer surplus is calculated as follows,

  $\text{Consumer surplus=}\frac{1}{2}\times Base\times Height$ ,

  $=\frac{1}{2}\times Q^{*}\times (P_m-P^{*})$

  $=0.5(200-140)(300)$

  $=\$9,000$

As the equilibrium price is increased, the consumer surplus will decreased by $7,000.

Now the producer surplus will be,

  $\text{Producer surplus=}\frac{1}{2}\times Base\times Height$

  $=\frac{1}{2}\times Q\times (P^{*}-P_s)$

  $=0.5(140-20)(480)$

  $=\$28,000$

As the equilibrium price is increased, producer surplus will increased by $8,800.

Now assume the equilibrium price is $95 then the consumer surplus will be,

  $\text{Consumer surplus=}\frac{1}{2}\times Base\times Height$

  $\begin{array}{l}=\frac{1}{2}\times Q^{*}\times (P_m-P^{*})\\ =0.5(200-95)(525)\\ =\$27,562.50\end{array}$

Thus consumer surplus is decreased by $11,562.50. Now the producer surplus will be,

  $\text{Producer surplus=}\frac{1}{2}\times Base\times Height$

  $\begin{array}{l}=\frac{1}{2}\times Q\times (P^{*}-P_s)\\ =0.5(95-20)(300)\\ =\$11,250\end{array}$

Thus, the producer surplus is decreased by $8,750.

Economics Concept Introduction

Introduction: Consumer surplus is the difference between the amount a consumer spends to purchase a commodity versus the amount he willingly wants to spend on the purchase.

Producer surplus is the difference between what the consumervoluntarily want to accept for a particular amount quantity of money or quantity of good and how much a person actually generates by selling the good in the market at the existing prices.

d.

To determine

To describe: The total loss of consumer and producer surplus, provided certain values are changed. Also, the total loss so incurred is independent of the price at which broccoli is sold has also to be determined.

Answer to Problem 9.7P

Thus the consumer surplus is increased by $2,000 and producer surplus is increased by $2,500.

Explanation of Solution

Let equilibrium quantity is Q=450, then consumer surplus will be,

  $\text{Consumer surplus=}\frac{1}{2}\times Base\times Height$

  $=\frac{1}{2}\times Q^{*}\times (P_m-P^{*})$

  $\begin{array}{l}=0.5(200-120)(450)\\ =\$18,000\end{array}$

Thus the consumer surplus is increased by $2,000. Now calculate the producer surplus,

  $\text{Producer surplus=}\frac{1}{2}\times Base\times Height$

  $\begin{array}{l}=\frac{1}{2}\times Q\times (P^{*}-P_s)\\ =0.5(120-20)(450)\\ =\$22,500\end{array}$

Thus the producer surplus is increased by $2,500.

Economics Concept Introduction

Introduction: Equilibriumpoint is that point at which demand and supply curve cut each other. At equilibrium quantity demanded is always equal to quantity supplied.

e.

To determine

To describe: The graph of results.

Answer to Problem 9.7P

The graphs of all the results are given below.

Explanation of Solution

  

  

  

Here, the price shows in Y-axis and quantity shows in X-axis. Here fig (a) shows the equilibrium point at 400 and the equilibrium price is $120. The fig (b) shows that the equilibrium price is reduced to 300 from 400. The blue area shows the loss. The fig (c) shows the variation in equilibrium price from $120 to $95. The fig(d) represents the increased quantity from 300 to 450.

Economics Concept Introduction

Introduction: Consumer surplus is a difference between the amount which consumer actually pays and the amount which he is willing to pay.

Producer surplus is the difference between what the consumer is willing to accept for a given quantity of money or good and the how much a person actually receives by selling the good in the market at the prevailing prices.