Chapter Notes

Here are the comprehensive study notes for the chapter "The Theory of the Firm under Perfect Competition".

The Theory of the Firm under Perfect Competition

This chapter explores a fundamental question in economics: how does a firm decide how much to produce? To answer this, we'll make a key assumption: a firm's main goal is to be a ruthless profit maximiser. This means it will produce and sell the exact amount of a good that makes its profit as large as possible.

We will first understand the specific market environment of perfect competition. Then, we will look at how a firm calculates its revenue and profit. Finally, we'll see how these principles help us derive a firm's supply curve (how much it's willing to sell at different prices) and the market supply curve (the total supply from all firms).

Perfect Competition: Defining Features

To understand a firm's decisions, we must first know the "rules of the game"—the market environment it operates in. We will focus on a market structure called perfect competition. It is defined by four main features:

• Large number of buyers and sellers: The market is filled with so many buyers and sellers that no single person or firm is big enough to influence the market price. Each one is like a tiny drop in a vast ocean.
• Homogenous product: Every firm sells an identical product. This means a buyer has no reason to prefer one firm's product over another's. Think of basic agricultural goods like wheat or milk; one farmer's wheat is essentially the same as another's.
• Free entry and exit for firms: Firms can easily start up and enter the market if they see an opportunity for profit, and they can just as easily leave if they are not successful. This is what ensures there can be a large number of firms.
• Perfect information: All buyers and sellers have complete information about the price, quality, and other details of the product. No one is tricked or has an unfair advantage because of secret knowledge.

These features lead to the single most important characteristic of perfect competition: price taking behaviour. Because no single firm can influence the market price, it must accept the prevailing market price as a given.

Revenue

A firm earns revenue by selling its product. In a perfectly competitive market, since the firm is a price-taker, the price it charges is simply the market price, which we'll call p.

Total Revenue (TR) is the total amount of money a firm receives from selling its output. It's calculated by multiplying the market price (p) by the quantity of the good sold (q).

• Formula: TR = p × q

Because the price (p) is constant for the firm, the Total Revenue curve is an upward-sloping straight line that starts from the origin (if you sell zero, you earn zero).

Average Revenue (AR) is the revenue per unit of output sold. It tells you how much revenue the firm earns on average for each unit.

• Formula: AR = TR / q
• Since TR = p × q, we can see that AR = (p × q) / q = p.

Marginal Revenue (MR) is the extra revenue earned from selling one additional unit of output.

• Formula: MR = Change in Total Revenue / Change in Quantity
• If a firm sells one more unit, it receives the market price (p) for that unit. Therefore, the extra revenue (MR) is simply the price.

This leads to a crucial conclusion for any firm in perfect competition: Price (p) = Average Revenue (AR) = Marginal Revenue (MR)

This relationship is represented graphically by the price line, which is a horizontal straight line at the level of the market price. This line is also the firm's demand curve, showing that it can sell any quantity it wants at the market price, making the demand perfectly elastic.

Profit Maximisation

A firm's profit is the difference between what it earns (Total Revenue) and what it spends (Total Cost). We use the Greek letter π (pi) to represent profit.

• Formula: Profit (π) = TR - TC

A firm wants to find the level of output that makes this gap between TR and TC the largest. For profit to be at its maximum, three conditions must be met.

1. Price must equal Marginal Cost (p = MC).

   • Think of it this way: As long as the revenue from selling one more unit (MR) is greater than the cost of making that unit (MC), producing it adds to your profit. So, you should keep producing.
   • If the cost of the next unit (MC) is more than the revenue it brings in (MR), producing it will reduce your profit. So, you should produce less.
   • The profit-maximising sweet spot is where the revenue from the last unit is exactly equal to its cost. Since p = MR in perfect competition, this condition becomes p = MC.

2. Marginal Cost (MC) must be non-decreasing.

   • The p = MC condition can sometimes happen at two output levels: once where the MC curve is falling, and once where it is rising. The firm will only maximise profit at the point where the MC curve is rising. If it were to produce where MC is falling, producing slightly less would actually increase its profit.

3. The firm must cover its costs to stay in business. This condition is slightly different for the short run and the long run.

   • In the short run: Price must be greater than or equal to the Average Variable Cost (p ≥ AVC). A firm has fixed costs (like rent) that it must pay even if it produces nothing. If the price is high enough to cover the variable costs of production (like raw materials) and contribute even a little bit towards the fixed costs, it's better to keep producing than to shut down and lose all the fixed costs. If the price falls below the minimum AVC, the firm can't even cover its operating costs, so it will shut down and produce zero.
   • In the long run: Price must be greater than or equal to the Average Cost (p ≥ AC). In the long run, all costs are variable, and a firm can exit the market. If the price is less than the average cost of production, the firm is making a loss and will eventually leave the industry.

Supply Curve of a Firm

A firm's supply curve shows the quantity of output it is willing to produce and sell at different market prices. We can derive this curve directly from the profit-maximisation conditions.

Short Run Supply Curve of a Firm

A firm's short-run supply curve is the rising portion of its Short run Marginal Cost (SMC) curve that lies at or above the minimum Average Variable Cost (AVC) curve.

• If the market price is below the minimum AVC, the firm will shut down and supply zero. This point is called the short run shut down point.
• If the market price is at or above the minimum AVC, the firm will produce at the point where p = SMC on the rising part of the SMC curve.

Long Run Supply Curve of a Firm

A firm's long-run supply curve is the rising portion of its Long run Marginal Cost (LRMC) curve that lies at or above the minimum Long run Average Cost (LRAC) curve.

• If the market price is below the minimum LRAC, the firm will exit the market and supply zero. The minimum point of the LRAC curve is the long run shut down point.
• If the market price is at or above the minimum LRAC, the firm will produce where p = LRMC on the rising part of the LRMC curve.

The Normal Profit and Break-even Point

• Normal Profit: This is the minimum level of profit an entrepreneur needs to earn to stay in their current business. You can think of it as the opportunity cost of running the firm—what the entrepreneur could have earned in their next best alternative. Normal profit is considered a part of the firm's total costs.
• Super-normal Profit: Any profit earned above the normal profit.
• Break-even Point: This is the point on the supply curve where a firm earns only normal profit (i.e., its profit is zero after accounting for all costs, including normal profit). This occurs where the price is equal to the minimum average cost (p = min AC).

Determinants of a Firm's Supply Curve

Since a firm's supply curve is a part of its marginal cost curve, any factor that changes the marginal cost will also shift the supply curve.

• Technological Progress: An improvement in technology allows a firm to produce more with the same inputs, or the same amount with fewer inputs. This lowers the cost of production, shifting the MC curve to the right (or downwards). As a result, the firm's supply curve shifts to the right, meaning it will supply more output at any given price.
• Input Prices: If the price of an input, like labour wages or raw materials, increases, the cost of production goes up. This shifts the MC curve to the left (or upwards). Consequently, the firm's supply curve shifts to the left, meaning it will supply less output at any given price.
• Impact of a Unit Tax: A unit tax is a tax the government imposes on each unit of a good sold. This tax directly increases the marginal cost of production by the amount of the tax. For example, a tax of Rs 2 per unit shifts the MC curve up by Rs 2. This causes the firm's supply curve to shift to the left.

Market Supply Curve

The market supply curve shows the total quantity of a good that all firms in the market are willing to supply at different prices.

It is derived by the horizontal summation of the individual supply curves of all the firms in the market. To find the market supply at a certain price, you simply add up the quantities that each individual firm is willing to supply at that price.

If more firms enter the market, the market supply curve will shift to the right. If firms exit the market, it will shift to the left.

Price Elasticity of Supply

The price elasticity of supply (eS) measures how responsive the quantity supplied of a good is to a change in its market price. It tells us the percentage change in quantity supplied for a one percent change in price.

• Formula: eS = (Percentage change in quantity supplied) / (Percentage change in price)

If eS > 1, supply is considered elastic. If eS < 1, supply is considered inelastic. If eS = 1, supply is unit elastic.

The Geometric Method

For a straight-line supply curve, you can determine its elasticity by looking at where it intersects the axes:

• Elastic Supply (eS > 1): A straight-line supply curve that intersects the price (vertical) axis will have an elasticity greater than 1.
• Unit Elastic Supply (eS = 1): A straight-line supply curve that passes through the origin will have an elasticity equal to 1 at all points.
• Inelastic Supply (eS < 1): A straight-line supply curve that intersects the quantity (horizontal) axis will have an elasticity less than 1.