Chapter 10, Problem 4P

Sub part (a):

To determine

Calculation of economic profit.

Explanation of Solution

Table -1 shows the data for the purely competitive producer

Table -1

Quantity	Average fixed cost	Average variable cost	Average total cost	Marginal cost
1	60	45	105
2	30	42.5	72.5	45
3	20	40	60	35
4	15	37.5	52	30
5	12	37	49	35
6	10	37.50	47.5	40
7	8.57	38.57	47.14	45
8	7.5	40.63	48.13	55
9	6.67	43.33	50	65
10	6	46.5	52.5	75

A profit maximizing firm produces output at the point where the marginal revenue equals to or greater than the marginal cost. Marginal revenue is equal to the price. At the price of $56, the marginal revenue is just greater than the marginal cost at the output level of 8 units. Thus, the profit maximizing output level is 8 units. At this point, the average variable cost is less than the price. Thus, the firm is operating in the short run.

Economic profit can be calculated as follows:

$\begin{array}{c}\text{Economic profit}=\left(\text{Price}\times \text{Quantity}\right)-\left(\text{Average total cost}\times \text{Quantity}\right)\\ =\left(56\times 8\right)-\left(48.13\times 8\right)\\ =448-385.04\\ =62.96\end{array}$

The economic profit is $62.96.

Economics Concept Introduction

Concept introduction:

Accounting profit: Accounting profit refers to the total revenue minus total explicit cost

Economic profit: Economic profit refers to the total revenue minus implicit and explicit cost.

Sub part (b):

To determine

Calculation of economic profit.

Explanation of Solution

At the price of $41, the marginal revenue is greater than the marginal cost at the output level of 6 units. Thus, the profit maximizing output level is 6 units. At this point, the average variable cost is less than the price. Thus, the firm is operating in the short run.

Economic profit can be calculated as follows:

$\begin{array}{c}\text{Economic profit}=\left(\text{Price}\times \text{Quantity}\right)-\left(\text{Average total cost}\times \text{Quantity}\right)\\ =\left(41\times 6\right)-\left(47.5\times 6\right)\\ =246-285\\ =-39\end{array}$

The economic profit is -$39.

Economics Concept Introduction

Concept introduction:

Accounting profit: Accounting profit refers to the total revenue minus total explicit cost

Economic profit: Economic profit refers to the total revenue minus implicit and explicit cost.

Sub part (c):

To determine

Shutdown decision.

Explanation of Solution

At the price of $32, the marginal revenue is greater than the marginal cost at the output level of 4 units. Thus, the profit maximizing output level is 8 units. At this point, the average variable cost ($37.5) is greater than the price. Thus, the firm will shutdown at this price. The firm’s economic loss is at the fixed cost $60.

Economics Concept Introduction

Concept introduction:

Pure competition: Perfect competition refers to the market structure featuring more number of sellers and buyers in the market where the firm can sell the homogenous products.

Profit maximizing output: Profit maximizing output occur at the point where the marginal revenue and marginal cost intersect each other.

Shutdown point: In the short run, a firm shuts down at the point where the price of goods is less than the average variable cost.

Sub part (d):

To determine

Average variable cost and profit maximization.

Explanation of Solution

Output at the price $26 is zero since the marginal revenue is less than the marginal cost at all the output levels.

Profit can be calculated by using the following formula.

$\text{Profit}=\left(\text{Price}\times \text{Quantity}\right)-\text{Fixed cost}-\left(\text{Average variable cost}\times \text{Quantity}\right)$ (1)

Substitute the respective values in equation (1) to calculate the profit at the price $26.

$\begin{array}{c}\text{Profit}=\left(\text{26}\times \text{0}\right)-60-\left(0\times \text{0}\right)\\ =-60\end{array}$

Thus, profit is -$60.

Quantity supply can be calculated by using the following formula.

$\text{Quantity}={\text{Quantity}}_{\text{Individual firm}}\times \text{Total number of firm}$ (2)

Substitute the respective values in equation (2) to calculate the total supply for 1,500 firms.

$\begin{array}{c}\text{Quantity}=0\times \text{1,500}\\ =0\end{array}$

Total supply at price $26 is 0 units.

Table -2 shows the output level obtained by using profit maximization condition $\left(\text{MR}\ge \text{MC}\right)$ . Also, it shows the profit or loss and the quantity supply that obtained by using the equations (1) and (2).

Table -2

Price	Quantity supplied for a single firm	Profit or loss	Quantity supplied for 1,500 firms
26	0	-60	0
32	0	-60	0
38	5	-55	7,500
41	6	-39	9,000
46	7	-7.98	10,500
56	8	62.96	12,000
66	9	144	13,500

Economics Concept Introduction

Concept introduction:

Pure competition: Perfect competition refers to the market structure featuring more number of sellers and buyers in the market where the firm can sell the homogenous products.

Profit maximizing output: Profit maximizing output occur at the point where the marginal revenue and marginal cost intersect each other.

Shutdown point: In the short run, a firm shuts down at the point where the price of goods is less than the average variable cost.

Sub part (e):

To determine

Supply schedule.

Explanation of Solution

Supply schedule refers to the total supply of the industry at different price levels. This can be derived from the Table -2, where column 1is price and column 4 is supply. This is given in the Table -3.

Table -3

Price	Quantity supply
26	0
32	0
38	7,500
41	9,000
46	10,500
56	12,000
66	13,500

Economics Concept Introduction

Concept introduction:

Supply schedule: Supply schedule refers to the table that shows the availability of supply at different price level.

Sub part (f):

To determine

Scenario for contraction in the production.

Explanation of Solution

Table -4 shows the demand and supply schedule.

Table -4

Price	Quantity demanded	Quantity supply
26	17,000	0
32	15,000	0
38	13,500	7,500
41	12,000	9,000
46	10,500	10,500
56	9,500	12,000
66	8,000	13,500

In Table -4, the market is in equilibrium at the point where the demand and supply is equal (10,500 units) at the price level $46. Thus, equilibrium price is $46 and equilibrium quantity is $10,500. Thus, the individual firm’s output is 7 $\left(\frac{10,500}{1500}\right)$ units. Profit is -$7.14 $\left(46-47.14\right)$ per firm. Since there is a loss, in the firm, there would be a contraction in the long run till it reaches a normal profit.