NCERT Solutions For Class 11 Economics Chapter 8 The Theory of the Firm under Perfect Competition

Market Price (p) is given as ₹10

Profit at each output level can be calculated by

Profit = TR – TC

To calculate TR, We use

TR = p × q

Price elasticity of supply measures the degree of responsiveness of quantity supplied to the changes in price of the good.

It is measured through

E^S = Elasticity of supply

ΔQ = change in quantity

ΔP = change in price

Q = initial Quantity supplied

P = initial market price

The increase in the number of firms in the market raises the total quantity supplied in the market. The increase in number of firms leads to a rightward shift in the market supply curve.

Imposition of a unit tax on per unit sale of output raises the average cost of for the firm. An increase in average cost of the product also increases the marginal cost of the firm. This leads to upward (or leftward) shift of the firms supply curve.

There are three necessary conditions for a profit maximizing firm to produce positive output in a competitive market.

1. Marginal cost = Marginal revenue
2. Marginal cost should be non- decreasing at the equilibrium output.
3. In the short run, price must be greater than the minimum level of AVC. In the long run, price must be greater than minimum level of AC.

The essential condition for profit maximizing firm to produce positive output is marginal revenue equal to marginal cost, which ensures that difference between total revenue and total cost is maximum.

Marginal revenue of a firm is defined as the increase in total revenue with an additional unit sold.

For a price taking firm, the market price of the good is fixed. When a firm increases its output by one unit, the extra unit sold is sold at the market price. Thus, the increase in total revenue due to additional unit sold is same as the market price.

MR = TR_{q + 1}  – TR_{q =} {P × (Q + 1) – PQ} = P

MR = P

Average revenue is defined as total revenue per unit of output.

For a price taking firm average revenue is equal to market price.

In a perfectly competitive market, price line is the line which determines the market price to be charged by the firms. Price line is a straight horizontal line which cuts the Y-axis, and depicts the demand curve for the perfectly competitive firm. In a perfectly competitive market all the firms are price taker. The market price is decided at the interaction of the market demand and market supply curve. At this market price a producer can sell any amount of quantity corresponding to the horizontal price line.

Total revenue of a firm is the revenue earned by a firm from sale of given quantity of the commodity. Total revenue of a firm is market price (p) multiplied by quantity sold of the output (q). Total revenue changes with the change in output produced by the firm.

TR = p × q

Given

Initial market price = 10

Final price = 30

Change in price (ΔP) = New price – Initial price = 30 – 10 = 20

Initial output = 4 units

Price elasticity of firm (E^s) = 1.25

Now, we substitute the above value into

Final output = initial output + change in output

                 = 4 + 10 = 14 units

The quantity firm will supply at the new price is 14 units.

Given

Initial market price = 5

Final price = 20

Change in price (ΔP ) = New price – Initial price = 20 – 5 = 15

Change in quantity (ΔQ ) = 15

Price elasticity of firm (E^s) = 0.5

Now, we substitute the above value into

Initial output is 10 units.

Now, Final output = Initial output + change in output

 = 10 + 15 = 25 units

The initial and final levels of output are 10 units and 25 units respectively.

Since all three firms are identical, all of them would have a similar supply schedule.

So, we can calculate market supply by

Market supply = 3 × SS₁ (units)

An increase in the price of an input leads to increase in average cost of production. Rise in average cost of production leads to rise in marginal costs of production at every level of output. The rise in marginal cost leads to upward shift (or leftward shift)of marginal cost curve. This means that the supply curve shifts to the left; at any given market price.

Technological process is taken as improvement in the production technology. For example if a firm uses same amount of capital & labour as inputs for production. Consider there is a technological progress which leads to improvement in production technology. Now, the firm can produce the same amount of output as earlier with less amount of labour and same amount of capital. This leads to reduction in average cost of the firm. Now as the average cost of the firm decreases, marginal cost also moves in the same direction. Thus, marginal cost and the average cost curve moves downward (or rightward). As a result, supply curve of the firm being a portion of firm marginal cost curve shifts rightward.

No, in the short run, a profit maximising firm would not produce positive level of output when the market price is less than the minimum of AVC.

At the market price (P₂) below AVC the firm would not be able to cover the variable cost of production and would earn losses from production of any output. So, firm would prefer not to produce positive output when market price is below average variable cost.

But, if the market price (P₁) is above AVC then the firm would produce Q₁level of positive output.

In a perfectly competitive market, market price of the good is fixed. Total revenue of the firm increases as the output of the firm goes up.

TR ↑ = p × q ↑

Total revenue of the firm increases with increase in each unit of output produced at the given price. Thus the total revenue curve of the price taking firm is upward sloping.

The total revenue curve passes through origin because at the zero level of output (q), total revenue is also zero.

TR = p × q

⇒ p × 0 = 0

Price elasticity of firm’s supply curve is degree of responsiveness of quantity supplied by the firm to the change in price in the market.

Formula for price elasticity for firm is

Change in price (ΔP ) = 15 – 10 = 5

Change in Quantity(ΔQ ) = 10 – 5 = 5

Price elasticity of the firm’s supply curve is 2.

Market supply can be calculated by

Market supply = SS₁ + SS₂

Market supply can be calculated by

Market supply = SS₁ + SS₂

Profit at each output level can be calculated by

Profit = TR – TC

And, market price at each level can be calculated by

Price = TR/Q

Given is the Market Price (P) = 10

To Calculate TR, MR and AR we use

TR = P × Q

MR = TR_Q+1 – TR_Q

AR = TR/q

The firm’s long run supply is the rising part of the LRMC curve from and above the minimum LRAC with zero output for all prices lesser than the minimum LRAC.

In the long run, if market price (P₂) is less than LRMC the firm would not produce any output as it incurs loss from production.The firm would only start producing positive level of output from the point where market price is equal to minimum point of LRAC. At this point LRMC = LRAC = P. From and above this point, firm will produce positive quantity of output and earn profit at corresponding price.Thus, the upward rising portion of LRMC, which is above minimum LRAC point, acts as the long run supply curve.

The short run supply curve of the firm is the rising part of the short-run marginal cost (SMC) from and above the minimum average variable cost curve with zero output level for all prices strictly less than the minimum AVC.

In the short run, when the price (P₂) is less than the AVC the firm would not produce any output as it would incur losses. But firm would produce Q1 level of output at the price (P1) as at this point (e) it is able to recover the variable cost of producing output. In the same manner firm produces positive output at point (f) where price is P3 and output is Q3. If we connect the point e and f we get a small portion of firm’s supply curve or SMC. If we keep increasing the market price we will get more points for the firm’s supply curve. These points are similar to the firm’s short-run marginal cost, thus the rising portion of MC above AVC is the supply curve of the firm.

No, a profit maximizing firm in a competitive market would not produce positive level of output in the long run if the market price is less than the minimum of AC.

In the long run, if price (P₁) is less than long run average cost, the firm would prefer to shut down its operation and exit the industry. At this price (P₁), the firm would incur losses in the long run (shown by the shaded region) and find it better to exit the industry rather than producing any positive amount of output.

At price (P₂), firm’s marginal revenue is equal to long run marginal cost and it would produce Q level of output. Below this market price the firm would incur losses but it will keep producing positive level of output in the short run if the price is greater than AVC. But in the long run, firm would not produce any output and would exit the industry.

There are three necessary conditions for a positive level of output to be produced by a profit maximising firm.

• Marginal cost = Marginal revenue
• Marginal cost should be non-decreasing at the equilibrium output.
• In the short run, price must be greater than the minimum level of AVC. In the long run, price must be greater than minimum level of AC.

A profit maximizing firm will not produce any positive level of output on the range where marginal cost is falling because producing on this range of marginal cost will lead to non-compliance of second condition given above i.e firm only produces positive level of output on non-decreasing part of the marginal cost curve.

In the diagram given below, profit maximising firm would not produce any quantity like Q₁ and Q₂ as it is on the decreasing or falling part of the marginal cost curve. The firm will only produce Q₃ level of output where all the above three conditions are satisfied.

There are three necessary conditions for a positive level of output to be produced by a profit maximizing firm.

• Marginal cost = Marginal revenue
• Marginal cost should be non- decreasing at the equilibrium output.
• In the short run, price must be greater than the minimum level of AVC. In the long run, price must be greater than minimum level of AC.

A perfectly competitive firm would only produce positive levels of output at a point where marginal revenue is equal to marginal cost. In case there is a disequilibrium i.e marginal cost is greater or lesser than the marginal revenue, the firm would not produce any positive level of output as it would lead to non-compliance with first condition given above. In the diagram given below, firm would only produce positive level of output Q* at point E.

The characteristics of a perfectly competitive market are:

1. Large number of buyers and sellers - There are large number of buyers and sellers in the market. A change in output supplied by a single firm does not affect the total output supplied in the market. The price for commodity is already given. At this price firms can supply any amount of output.
2. Firms are price taker- Firms in a perfectly competitive market are‘price taker’ and industry is the ‘price maker’. Price in this market is determined by market demand and supply of the industry.
3. Homogeneous product -The commodity produced by each firm are identical in all the aspects shape,size,quality,etc. Goods produced by all the firms are perfect substitute for each other.
4. Free entry and exit - Firms are free to enter or exit the market. There are no barriers involved during the entry or exit from the industry.
5. Perfect knowledge - All the individuals or players have perfect knowledge about the product market as well as the factor market. This perfect knowledge also extends to technology. Every firm in the perfectly competitive market has access to same production technology.
6. Perfect mobility of factors of production - Factors of production are free to move from one firm to another.
7. Absence of transportation cost - All the goods are locally produced, thus no or negligible transportation cost.