Chapter 3, Problem 5.7P

Subpart (a):

To determine

Graph the supply and demand schedule for pizza.

Explanation of Solution

The calculation of quantity demanded (${\text{Q}}_{\text{d}}$) is shown below:

${\text{Q}}_{\text{d}}=300-20\text{P}$ (1)

Substitute the values in equation (1) to calculate the quantity demanded at price $5.

$\begin{array}{c}{\text{Q}}_{\text{d}}=300-20\left(5\right)\\ =300-100\\ =200\end{array}$

Quantity demanded is 200.

The calculation of quantity supplied (${\text{Q}}_{\text{s}}$) is shown below:

${\text{Q}}_{\text{s}}=20\text{P}-100$ (2)

Substitute the values in equation (1) to calculate the quantity supplied at price $0.5.

$\begin{array}{c}{\text{Q}}_{\text{s}}=20\left(5\right)-100\\ =100-100\\ =0\end{array}$

The quantity supplied is 0.

By using the same Equation (1) and (2), the supply demand schedule is shown in Table 1.

Table 1

Price	Quantity demanded	Quantity supplied
$5	200	0
$10	100	100
$15	0	200

On the basis of the above demand schedule, the supply and demand curve of pizza is shown below.

Figure 1 shows equilibrium price and quantity of pizza.

In Figure 1, the vertical axis measures the price of pizza and horizontal axis measures the quantity demanded of pizza. The downward sloping curve is the demand curve and upward sloping curve is the supply curve of pizza. The intersecting point of the demand and supply curve is the equilibrium point and the corresponding price and quantity is the equilibrium price and equilibrium quantity of pizza. Thus, $10 is the equilibrium price and 100 is the equilibrium quantity of pizza.

Economics Concept Introduction

Concept introduction:

Equilibrium point: Intersecting point of demand and supply is known as equilibrium point and corresponding price and quantity is the equilibrium price and equilibrium quantity.

Subpart (b):

To determine

Calculation of quantity of pizza.

Explanation of Solution

The given information:

${\text{Q}}_{\text{d}}=300-20\text{P}$

${\text{Q}}_{\text{s}}=20\text{P}-100$

Calculation:

The calculation of quantity of pizza is shown below:

$\begin{array}{c}{\text{Q}}_{\text{d}}={\text{Q}}_S\\ 300-20\text{P}=\text{20P}-100\end{array}$

Substitute the values of price as $10 either the demand or supply equation.

$\begin{array}{c}{\text{Q}}_{\text{d}}=300-20\left(10\right)\\ =300-200\\ =100\end{array}$

The quantity demanded of pizza is 100 at price $10.

Economics Concept Introduction

Concept introduction:

Demand: Consumer's desire and willingness to pay a price for a specific good or service which satisfies his wants.

Subpart (c):

To determine

Effect of change in price of pizza on its supply.

Explanation of Solution

If the suppliers set the price of pizza at $15, the producer would want to produce 200 pizzas $\left(20\times 15-100=200\right)$. Since there is a surplus amount of pizza, the price has to come down to increase the demand, while decreasing the price of the supply of goods decreases. This process will continue till the point where demand is equal to the supply.

Subpart (d):

To determine

Equation for new market demand.

Explanation of Solution

When the price of hamburgers (substitute for pizza) doubles, the quantity demanded of pizza will change. Thus, the equation for new market demand for pizza is shown below:

${\text{Q}}_{\text{d}}=600-40\text{P}$

Subpart (e):

To determine

Calculation of equilibrium price and quantity.

Explanation of Solution

The given information:

${\text{Q}}_{\text{d}}=600-40\text{P}$

Calculation:

The calculation of equilibrium quantity (${\text{Q}}_{\text{d}}$) is shown below. Substitute the values in new market equation as follows:

$\begin{array}{c}{\text{Q}}_{\text{d}}={\text{Q}}_{\text{S}}\\ 600-40\text{P}=20\text{P}-\text{100}\\ \text{=}\frac{\text{600+100}}{40-\left(-20\right)}\\ =\frac{700}{60}\\ =11.67\end{array}$

The equilibrium price is $11.67.

Substitute the values of price either demand od supply equation to calculate  the equilibrium quantity as follows:

$\begin{array}{c}{\text{Q}}_{\text{d}}=600-40\left(11.67\right)\\ =600-466.8\\ =133.2\end{array}$

The equilibrium quantity is 133.

Economics Concept Introduction

Concept introduction:

Equilibrium point: Intersecting point of demand and supply is known as equilibrium point and corresponding price and quantity is the equilibrium price and equilibrium quantity.