The Theory of the Firm under Perfect Competition

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The characteristics of a perfectly competitive market are:

These characteristics lead to the single most distinguishing characteristic of perfect competition: price-taking behavior. A price-taking firm believes that if it sets a price above the market price, it will be unable to sell any quantity of the good that it produces. Conversely, if the set price is less than or equal to the market price, the firm can sell as many units of the good as it wants to sell.

The total revenue (TR) of a firm, market price (p), and the quantity sold by the firm (q) are related to each other in the following way:

The relationship between these three can be depicted using a Total Revenue Curve, where the quantity sold is on the X-axis and the revenue earned is on the Y-axis. The curve is a straight line because the price is constant in a perfectly competitive market, making the TR curve an upward rising straight line.

Additionally, the Average Revenue (AR) of a firm is defined as total revenue per unit of output, which equals the market price {\left(AR = \dfrac{TR}{q} = p\right)}. The Marginal Revenue (MR) of a firm is the increase in total revenue for a unit increase in the firm’s output, and for a perfectly competitive firm, MR equals the market price (MR = p).

The ‘price line’ is a concept in economics that refers to a horizontal straight line on a graph that represents the market price of a product in a perfectly competitive market. Here’s how it is related to a firm under perfect competition:

Therefore, the price line is a graphical representation of the constant price at which a firm can sell its products in a perfectly competitive market. It is horizontal because the price does not change with the quantity of goods sold, reflecting the fact that firms in such markets are price takers.

The total revenue curve of a price-taking firm is an upward-sloping straight line because the total revenue (TR) is calculated by multiplying the market price (p) by the quantity sold (q). In a perfectly competitive market, the price is constant regardless of the quantity sold. Therefore, as the quantity sold increases, the total revenue increases at a constant rate, which is represented graphically by a straight line with a positive slope.

The total revenue curve passes through the origin because when the quantity sold is zero, the total revenue is also zero. This is intuitive because if a firm does not sell any goods, it does not generate any revenue. The equation TR = p × q translates into a straight line that begins at the origin (0, 0) on a graph where the x-axis represents quantity and the y-axis represents revenue.

To summarize, the total revenue curve is a straight line with a slope equal to the market price (p), and it passes through the origin because the total revenue is zero when no goods are sold.

The relationship between market price and average revenue for a price-taking firm is direct and straightforward: for a price-taking firm, the average revenue (AR) equals the market price (p). This is because a price-taking firm in a perfectly competitive market has no control over the price of the product it sells; it must accept the market price.

The average revenue is calculated as the total revenue (TR) divided by the quantity (q) of goods sold. Since the total revenue is the product of the market price and the quantity sold (TR = p × q), when you divide the total revenue by the quantity, the quantity terms cancel out, leaving you with the market price. Therefore, {AR = \dfrac{TR}{q} = \dfrac{(p × q)}{q} = p}.

This means that the average revenue curve for a price-taking firm is a horizontal line at the level of the market price, which is also referred to as the ‘price line’. This line reflects the fact that the firm can sell any quantity of its product at this price.

For a price-taking firm in a perfectly competitive market, the marginal revenue (MR) is equal to the market price (p). This is because the firm can sell additional units of its product at the market price without affecting the price itself.

Marginal revenue is the additional revenue that a firm earns by selling one more unit of a product. In a perfectly competitive market, when a firm sells one more unit, it does so at the market price, which means the increase in total revenue from selling that additional unit (which is the definition of MR) is exactly the market price.

Therefore,

This relationship is a key characteristic of perfect competition and indicates that the MR curve for a price-taking firm is also a horizontal line at the market price, just like the average revenue curve.

In a competitive market, it is generally the case that for a profit-maximising firm to produce a positive level of output, the market price must be equal to the marginal cost (P = MC). This is because the firm will increase its output until the point where the cost of producing one more unit (marginal cost) is exactly covered by the revenue from selling that unit (price). Producing beyond this point would mean the cost of producing an additional unit is greater than the revenue it would bring, which would decrease profits.

However, there could be a special scenario where a profit-maximising firm produces a positive level of output where the market price is not equal to marginal cost. This could occur if there are constraints or imperfections in the market that prevent the firm from adjusting its output instantly or if there are fixed costs that need to be covered in the short run. For instance, if the firm has already invested in a fixed cost that cannot be recovered in the short term (sunk cost), it might continue to produce as long as the price covers the average variable cost, even if the price does not cover the average total cost, which includes both variable and fixed costs.

In the short run, a firm may decide to produce even if the price is below the average total cost but above the average variable cost, because by contributing to the fixed costs, it reduces losses compared to not producing at all. In the long run, however, the firm would need to cover the full average cost to be profitable and remain in the market.

In a competitive market, a profit-maximising firm will not produce at an output level where the market price is lower than the average cost (AC) in the long run. This is because, at such an output level, the firm’s total revenue (TR) would be less than its total cost (TC), leading to a loss. In the long run, a firm that shuts down production has a profit of zero, and it would choose to exit the market rather than incur a loss.

Therefore, for a profit-maximising firm in a competitive market, the market price must be greater than or equal to the average cost (AC) in the long run for it to produce a positive level of output. If the market price is less than the AC, the firm will not supply any output.

In the short run, however, the condition is slightly different. The price must be greater than or equal to the average variable cost (AVC) for the firm to continue production. If the market price falls below the AVC, the firm is better off shutting down production in the short run.

In summary, for a profit-maximising firm in a competitive market:

A profit-maximizing firm in a competitive market will not produce a positive level of output at a point where the marginal cost (MC) is falling. This is because, for profit maximization, the firm’s output level must satisfy three conditions:

Specifically addressing the second condition, the document states that the marginal cost curve cannot slope downwards at the profit-maximizing output level. If the marginal cost were decreasing, it would imply that for output levels slightly less than the profit-maximizing output level, the marginal cost would be higher than the price, which contradicts the profit-maximizing principle that marginal revenue (MR) should equal marginal cost (MC).

Therefore, a profit-maximizing firm in a competitive market will not produce a positive level of output in the range where the marginal cost is falling because it would not satisfy the necessary condition for profit maximization—that the marginal cost must be non-decreasing at the profit-maximizing output level.

A profit-maximising firm in a competitive market will not produce a positive level of output in the short run if the market price is less than the minimum of the average variable cost (AVC). The explanation for this is based on the concept of the shutdown point.

The shutdown point is the level of pricing at which a firm ceases to produce in the short run. This occurs at the price-output combination where the price is equal to the minimum of the AVC. If the market price falls below this minimum AVC, the firm’s total revenue from producing any positive output would not cover its variable costs. Producing at a loss is not sustainable, even in the short term, because the firm would lose less money by shutting down and avoiding variable costs altogether.

In essence, if the market price is below the minimum AVC, the firm would incur a smaller loss by not producing anything, as its loss would be limited to its fixed costs, which have to be paid regardless of the level of output. Therefore, in the short run, a profit-maximising firm will produce zero output if the market price is less than the minimum AVC.

A profit-maximising firm in a competitive market will not produce a positive level of output in the long run if the market price is less than the minimum of average cost (AC). The explanation for this is grounded in the firm’s need to cover all of its costs in the long run to remain in business.

In the long run, all costs are variable, and there are no fixed costs. Therefore, the average cost includes all costs associated with production. If the market price is below the minimum average cost, the firm cannot cover its production costs, let alone make a profit. Producing under these conditions would lead to a loss with each unit of output sold because the revenue from selling the product at the market price would be less than the cost of producing it.

Consequently, in the long run, a firm will exit the market if it cannot produce at a level where the market price is at least equal to the minimum average cost. This ensures that the firm can cover its costs and make a non-negative economic profit. If the market price is below this level, the firm’s best response is to produce zero output and potentially shut down, as any production would result in a loss.

The supply curve of a firm in the short run represents the quantity of goods that a firm is willing and able to produce and sell at each possible market price, given its existing plant size and fixed factors of production.

Here are the key characteristics of a firm’s short run supply curve:

In summary, the short run supply curve of a firm in a competitive market is the upward-sloping part of the marginal cost curve that lies above the average variable cost curve.

The supply curve of a firm in the long run reflects the quantity of goods that a firm is willing to produce and sell at each possible market price when all factors of production are variable, and the firm can adjust all inputs freely. This means the firm can change its plant size and enter or exit the industry in response to market conditions.

Here are the key characteristics of a firm’s long run supply curve:

In essence, the long run supply curve of a firm in a competitive market is the segment of the LRMC curve that is above the minimum point of the LRAC curve, indicating the range of prices at which the firm is willing to supply output when it is free to adjust all of its inputs and production capacity.

Technological progress affects the supply curve of a firm by shifting it to the right (or downward). This shift occurs because technological advancements typically lead to improvements in production efficiency. Here’s how it works:

In summary, technological progress typically leads to a more efficient production process, which lowers the marginal cost of production and results in a rightward shift of the firm’s supply curve. This means that at any given price level, the firm is able to supply a greater quantity of goods.

The imposition of a unit tax affects the supply curve of a firm by shifting it to the left (or upward). A unit tax is a tax imposed by the government on each unit of a good produced by the firm. Here’s the impact of a unit tax on the firm’s supply curve:

In essence, a unit tax increases the cost of production per unit, which causes the firm to supply a smaller quantity of goods at any given price level, resulting in a leftward shift of the supply curve.

An increase in the price of an input affects the supply curve of a firm by shifting it to the left (or upward). Here’s how this works:

In summary, an increase in the price of an input leads to higher production costs, which in turn increases the marginal cost of production. This results in a leftward shift of the firm’s supply curve, indicating that the firm will supply less at every price level.

An increase in the number of firms in a market affects the market supply curve by shifting it to the right (or downward). Here’s the rationale behind this shift:

In essence, an increase in the number of firms in a market typically leads to a rightward shift in the market supply curve, indicating that a larger quantity of the good will be supplied at each price level.

The price elasticity of supply (ES) measures the responsiveness of the quantity supplied of a good or service to a change in its price. It is a measure of how much the supply of a good is affected by changes in its price.

Here’s how the price elasticity of supply is defined and measured:

Understanding the price elasticity of supply is crucial for businesses and policymakers as it affects pricing strategies, taxation policies, and how markets respond to changes in supply conditions.

To compute the Total Revenue (TR), Marginal Revenue (MR), and Average Revenue (AR) for each quantity sold at a market price of ₹ 10, we can use the following formulas:

Given that the market price is constant at ₹ 10, the Marginal Revenue (MR) will be equal to the market price for each additional unit sold, because the addition to total revenue by selling one more unit is just the price at which that unit is sold.

Let’s compute the values for each quantity sold:

In this case, because the price is constant, the Marginal Revenue and Average Revenue remain constant at ₹ 10, which is equal to the market price. Total Revenue increases by ₹ 10 for each additional unit sold.

Profit is calculated as Total Revenue (TR) minus Total Cost (TC). Let’s calculate the profit at each output level:

Now, to determine the market price of the good, we look at the total revenue for each additional unit sold. In a competitive market, the price per unit is constant, and the total revenue increases by this price with each additional unit sold.

From the table, we can see that the total revenue increases by ₹ 5 for each additional unit sold (from ₹ 0 to ₹ 5, ₹ 5 to ₹ 10, and so on). This implies that the market price of the good is ₹ 5 per unit.

Also, we can see that the firm makes a profit at quantities 3, 4, and 5, with the highest profit of ₹ 5 occurring at a quantity of 4 units sold. At other quantities, the firm either breaks even (quantity 2) or incurs a loss.

To calculate the profit at each output level, we need to subtract the total cost (TC) from the total revenue (TR) at each level of output. Since the price of the good is given as ₹ 10, the total revenue at each output level can be calculated by multiplying the output by the price (P).

Let’s calculate the profit for each output level:

Now, to find the profit-maximising level of output, we look for the output level with the highest profit. From the table, we can see that the maximum profit of ₹ 12 is at an output level of 5 units.

Therefore, the profit-maximising level of output for the firm is 5 units.

The market supply schedule is obtained by adding the supply schedules of the individual firms at each price level. To compute the market supply schedule, we simply sum the quantities supplied by firm 1 (SS1) and firm 2 (SS2) at each price.

Here is the market supply schedule based on the given data:

So, at a price of ₹ 3, the market supply is 2 units; at a price of ₹ 4, the market supply is 4 units; and this pattern continues, with the market supply increasing by 2 units for each ₹ 1 increase in price.

To compute the market supply schedule, we add the supply from firm 1 (SS1) and firm 2 (SS2) at each price level. Here’s the market supply schedule based on the given data:

The market supply at each price level is the sum of the supplies from both firms.

If there are three identical firms in the market, each with the same supply schedule as firm 1, then the market supply schedule is simply three times the supply of firm 1 at each price level. We can calculate the market supply by multiplying the supply from firm 1 (SS1) by 3.

Here’s the market supply schedule based on the given data:

The market supply at each price level is the aggregate of the supplies from all three firms.

The price elasticity of supply (ES) measures the responsiveness of the quantity supplied to a change in price. It is calculated using the formula:

First, we need to calculate the percentage change in quantity supplied and the percentage change in price.

From the information given:

Since Revenue = Price × Quantity, we can calculate the initial and final quantities supplied Q1 and Q2:

Now we calculate the percentage changes:

Substituting the values:

Finally, we calculate the ES:

The price elasticity of the firm’s supply curve is 2, which means the supply is elastic. For every 1% increase in price, the quantity supplied increases by 2%.

The price elasticity of supply (ES) is given by the formula:

We are given:

First, we need to calculate the percentage change in price:

Substituting the values:

Now we can use the ES formula to find the percentage change in quantity supplied:

Solving for the percentage change in quantity supplied:

This means the quantity supplied increased by 150% of the initial quantity supplied. To find the initial quantity supplied Q1, we use the fact that a 150% increase corresponds to the 15 units increase we have:

1.5 × Q1 = 15 units

Solving for Q1:

Now that we have the initial quantity supplied, we can find the final quantity supplied Q2 by adding the change in quantity supplied to the initial quantity:

So, the initial output level of the firm was 10 units, and the final output level was 25 units.

The price elasticity of supply (ES) is given by the formula:

We are given:

First, we need to calculate the percentage change in price:

Substituting the values:

Now we can use the PS formula to find the percentage change in quantity supplied:

Solving for the percentage change in quantity supplied:

This means the quantity supplied increased by 250% of the initial quantity supplied. To find the change in quantity supplied ΔQ, we use the fact that a 250% increase corresponds to the change in quantity supplied based on the initial quantity:

Now we can find the final quantity supplied Q2 by adding the change in quantity supplied to the initial quantity:

So, at the new price of ₹ 30, the firm will supply 14 units of output.