Chapter 13, Problem 10P

(a)

To determine

Market demand function of flour.

Explanation of Solution

Given information:

The marginal revenue product of flour is ${\text{MRP}}_{\text{F}}=6\text{0}-\text{0}\text{.01Q}$ (1)

Calculation:

The inverse demand function is shown below:

$\text{P}=6\text{0}-\text{0}\text{.01Q}$ (2)

From the inverse demand equation, the demand equation of each individual baker can be derived as follows:

$\begin{array}{c}\text{P}=6\text{0}-\text{0}\text{.01Q}\\ \text{0}\text{.01Q}=6\text{0}-\text{P}\\ \text{Q}=\frac{6\text{0}}{0.01}-\frac{\text{P}}{0.01}\end{array}$

$\text{Q}=6,000-100\text{P}$ (3)

The demand equation for each individual baker is$\text{Q}=6,000-100\text{P}$.

To find the whole market demand for flour, multiply Equation (3) by 1,000. (Total number of producers).

$\text{Q}=6,000,000-1000,00\text{P}$ (4)

The whole demand for the market for flour is$\text{Q}=6,000,000-1000,00\text{P}$.

Economics Concept Introduction

Demand: Demand is the quantity of goods and services that people are willing and able to buy at particular price in a given period of time.

(b)

To determine

Calculate the equilibrium price.

Explanation of Solution

Given information:

The market supply function for flour is ${\text{Q}}_{\text{S}}=\text{150,000P}$.

Calculation:

The intersecting point of supply and demand is the equilibrium point. The corresponding price in the equilibrium point is the equilibrium price. Equate the market demand equation (Equation (4) derived in part (a)) and supply equation to calculate the equilibrium price of flour.

$\begin{array}{c}{\text{Q}}_{\text{S}}={\text{Q}}_{\text{D}}\\ \text{150,000P}=6,000,000+1000,00\text{P}\\ \text{150,000P}+1000,00\text{P}=6,000,000\\ \text{250,000P}=6,000,000\\ \text{P}=\frac{6,000,000}{\text{250,000}}\\ \text{P}=24\end{array}$

Equilibrium price is $24.

Economics Concept Introduction

Equilibrium price:  The equilibrium price is the market price determined by the interaction between the quantity demanded and the quantity supplied.

(c)

To determine

Equilibrium quantity of bread.

Explanation of Solution

Substitute the equilibrium price in the demand equation (Equation (3) derived in part (a)) to calculate the equilibrium quantity of flour demanded.

$\begin{array}{l}\text{Q}=6,000-100\text{P}\\ \text{Q}=6,000-100\left(24\right)\\ \text{Q}=6,000-2,400\\ \text{Q}=3,600\end{array}$

Equilibrium quantity is 3,600 units of flour.

Economics Concept Introduction

Equilibrium quantity: The equilibrium quantity is the point where the quantity demanded is equal to the quantity supplied.

(d)

To determine

Total market quantity of flour demanded.

Explanation of Solution

Substitute the equilibrium price in the market demand equation (Equation (4) derived in part (a)) to calculate the market quantity.

$\begin{array}{l}\text{Q}=6,000,000-1000,00\text{P}\\ \text{Q}=6,000,000-1000,00\left(24\right)\\ \text{Q}=6,000,000-24,00,000\\ \text{Q}=36,00,000\end{array}$

Total market quantity of flour is 36, 00,000 units of flour; thus, each of 1000 bakers buy 3,600 units.

(a)

To determine

New market demand function of flour, new equilibrium price and quantity, and quantity of bread flour purchased by each baker.

Explanation of Solution

Given information:

The marginal revenue product of flour is ${\text{MRP}}_{\text{F}}=6\text{0}-\text{0}\text{.02Q}$ (5)

Calculation:

The inverse demand function is shown below.

$\text{P}=6\text{0}-\text{0}\text{.02Q}$ (6)

From the new inverse demand equation, the demand equation for each individual baker can be derived as follows:

$\begin{array}{c}\text{P}=6\text{0}-\text{0}\text{.02Q}\\ \text{0}\text{.02Q}=6\text{0}-\text{P}\\ \text{Q}=\frac{6\text{0}}{0.02}-\frac{\text{P}}{0.02}\end{array}$

$\text{Q}=3,000-50\text{P}$ (7)

The new demand equation for each individual baker is$\text{Q}=3,000-50\text{P}$.

To find the whole market demand for flour, multiply Equation (7) by 1000.

$\text{Q}=3,000,000-50,000\text{P}$ (8)

The whole demand for the market is $\text{Q}=3,000,000-50,000\text{P}$.

The intersecting point of supply and demand is the equilibrium point. The corresponding price in the equilibrium point is the equilibrium price. Equate the market demand equation (Equation (7) and supply equation to calculate the new equilibrium price of flour.

$\begin{array}{c}{\text{Q}}_{\text{S}}={\text{Q}}_{\text{D}}\\ \text{150,000P}=3,000,000+50,000\text{P}\\ \text{150,000P}+50,000\text{P}=3,000,000\\ \text{250,000P}=3,000,000\\ \text{P}=\frac{3,000,000}{\text{200,000}}\\ \text{P}=15\end{array}$

New equilibrium price is $15.

Substitute the new equilibrium price in the new market demand equation (Equation (8) to calculate the new market quantity.

$\begin{array}{l}\text{Q}=3,000,000-50,000\text{P}\\ \text{Q}=3,000,000-50,000\left(15\right)\\ \text{Q}=3,000,000-750,000\\ \text{Q}=2,250,000\end{array}$

The new market quantity of flour is 2,250,000 units of flour; thus, each of 1000 bakers buy 2,250 units.

Economics Concept Introduction

Demand: Demand is the quantity of goods and services that people are willing and able to buy at particular price in a given period of time.

Equilibrium price:  The equilibrium price is the market price determined by the interaction between the quantity demanded and the quantity supplied.

Equilibrium quantity: The equilibrium quantity is the point where the quantity demanded is equal to the quantity supplied.