Chapter 8, Problem 13P

(a)

To determine

The individual supply curve.

Explanation of Solution

It is given the marginal cost of rainy season growers is $\text{MC}=.02\text{Q}$ and the marginal cost of dry season growers is $\text{MC}=.04\text{Q}$.

The quantity supplied by each almond grower is the quantity at which the price is equal to the marginal cost.

$\text{P}=\text{MC}$

The quantity supplied by rainy area growers can be calculated as follows:

$\begin{array}{c}{\text{P}}_{\text{R}}=0.\text{02Q}\\ \text{Q}=\frac{{\text{P}}_{\text{R}}}{0.02}\\ \text{Q}=50{\text{P}}_{\text{R}}\end{array}$

Thus, the quantity supplied by rainy area growers is $\text{Q}=50{\text{P}}_{\text{R}}$.

The quantity supplied by dry area growers can be calculated as follows:

$\begin{array}{c}{\text{P}}_{\text{D}}=0.\text{04Q}\\ \text{Q}=\frac{{\text{P}}_{\text{D}}}{0.04}\\ \text{Q}=25{\text{P}}_{\text{D}}\end{array}$

Thus, the quantity supplied by dry area growers is $\text{Q}=25{\text{P}}_{\text{D}}$.

Economics Concept Introduction

Supply: Supply is defined as the quantity of a commodity offered for sale at different market prices.

(b)

To determine

The market supply.

Explanation of Solution

The market supply function can be obtained as the sum of the product of number of producers in each category with their respective individual supply function.

$\begin{array}{c}\text{Quantity supplied}=\left(\begin{array}{c}\left(\begin{array}{l}\text{Number of growers in rainy area}\\ \times \text{Quantity supplied by rainy area growers}\end{array}\right)\\ +\left(\begin{array}{l}\text{Number of growers in dry area}\\ \times \text{Quantity supplied by dry area growers}\end{array}\right)\end{array}\right)\\ =500\left(50\text{P}\right)+300\left(25\text{P}\right)\\ =25,000\text{P}+7,500\text{P}\\ =32,500\text{P}\end{array}$

Thus, the market supply is 32,500P.

Economics Concept Introduction

Supply: Supply is defined as the quantity of a commodity offered for sale at different market prices.

(c)

To determine

The equilibrium price and quantity.

Explanation of Solution

When the market is in equilibrium, the market demand is equal to the market supply.

It is given that the market demand is ${\text{Q}}_{\text{d}}=105,000-2,500\text{P}$.

$\begin{array}{c}\text{Quantity demanded}=\text{Quantity supplied}\\ 105,000-2,500\text{P}=32,500\text{P}\\ 105,000=32,500\text{P}+2,500\text{P}\\ 105,000=35,000\text{P}\\ \text{P}=\frac{105,000}{35,000}\\ =3\end{array}$

The equilibrium price in the market is $3.

Substituting the value of price in the demand function, the quantity demanded at equilibrium can be calculated as follows:

$\begin{array}{c}{\text{Q}}_{\text{d}}=105,000-2,500\left(3\right)\\ =105,000-7,500\\ =97,500\end{array}$

Thus, the equilibrium quantity is 97,500.

Economics Concept Introduction

Supply: Supply is defined as the quantity of a commodity offered for sale at different market prices.

(d)

To determine

The quantity of almonds produced.

Explanation of Solution

The total quantity of almonds produced by rainy area growers is as follows:

$\begin{array}{c}\text{Quantity supplied}=\left(\text{Number of growers in rainy area}\times \text{Quantity supplied by rainy area growers}\right)\\ =500\left(50\text{P}\right)\\ =25,000\text{P}\\ =25,000\left(3\right)\\ =75,000\end{array}$

The total quantity of almonds produced by rainy area growers is 75,000 crates.

The total quantity of almonds produced by dry area growers is as follows:

$\begin{array}{c}\text{Quantity supplied}=\left(\text{Number of growers in dry area}\times \text{Quantity supplied by dry area growers}\right)\\ =300\left(\text{25P}\right)\\ =7,500\text{P}\\ =7,500\left(3\right)\\ =22,500\end{array}$

The total quantity of almonds produced by dry area growers is 22,500 crates.

(e)

To determine

Whether the total production of all almond growers is equal to the market supply.

Explanation of Solution

The total quantity of almond produced by all almond growers is calculated as follows:

$\begin{array}{c}\text{Total quantity of almond produced}=\left(\begin{array}{l}{\text{Quantity supplied}}_{\text{Rainy area growers}}\\ +{\text{Quantity supplied}}_{\text{Dry area growers}}\end{array}\right)\\ =75,000+22,500\\ =97,500\end{array}$

Thus, the total quantity of almonds supplied by all almond growers is 97,500. This is equal to the market supply obtained in part (c).

Economics Concept Introduction

Supply: Supply is defined as the quantity of a commodity offered for sale at different market prices.