How does the imposition of a unit tax affect the supply curve of a firm?

Exercises · Q15

Q. How does the imposition of a unit tax affect the supply curve of a firm?

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Concept understanding — Short Run Supply Curve

The Short Run Supply Curve: From a Lemonade Stand to Market Logic

Imagine you run a small lemonade stall. One hot afternoon, a customer offers you ₹50 for a glass — your usual price is ₹20. Do you sell it? Of course you do. But what if the price drops to ₹5? You'd probably refuse, because the cost of lemons, sugar, and your time is more than that.

This instinct — sell more when price is high, sell less (or nothing) when price is low — is the seed of the supply curve. But in economics, we need to be precise about when this logic applies.

The Precise Meaning

The Short Run Supply Curve of a firm shows the quantity of output a profit-maximising firm is willing to supply at each possible market price, when at least one factor of production is fixed (typically capital — factory size, machinery). In the short run, the firm cannot change its plant size; it can only vary variable inputs like labour and raw materials.

Important

The short run supply curve of a perfectly competitive firm is that portion of its Marginal Cost (MC) curve which lies above the Average Variable Cost (AVC) curve.

Why this specific part? Because the firm's decision rule is simple: produce as long as the price covers the variable cost of production. Fixed costs (rent, loan payments) are already sunk — they exist whether the firm produces or not.

The Logic Behind the Shape

The supply curve slopes upward in the short run. Here's why:

Diminishing returns: As you hire more workers on a fixed factory floor, each additional worker adds less to output than the previous one. So to produce one more unit, you need more and more labour — raising the marginal cost.
Profit-maximisation rule: A firm produces where $P = MC$ (price equals marginal cost). As price rises, the firm moves up its MC curve, producing more.
Shutdown point: If price falls below the minimum of AVC, the firm cannot even cover its variable costs. It's better to shut down (produce zero) and only lose fixed costs. So the supply curve starts only from the point where $P \geq \text{min } AVC$ .

Watch out

A common mistake: thinking the supply curve is the entire MC curve. It is not. The portion below the AVC curve is irrelevant — the firm would never produce there.

Diagram in Words

Draw the standard cost curves:

MC curve: U-shaped, rising steeply after a point.
AVC curve: U-shaped, lying below the Average Total Cost (ATC) curve.
The short run supply curve is the rising portion of MC from the point where it cuts the AVC curve (the minimum point of AVC) and continues upward.

At any price below this intersection, supply is zero. At any price above it, the firm supplies the quantity where $P = MC$ .

Why It Matters

The short run supply curve is not just a textbook abstraction. It explains real-world behaviour:

Why farmers sometimes destroy crops: If market price falls below variable cost, it's rational to not harvest — even if fixed costs (land, equipment) are already paid. …

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A unit tax (a fixed amount per unit sold) shifts the firm's supply curve vertically upward by exactly the amount of the tax, because the firm now requires a higher market price to cover both production cost and the tax for each quantity.

The supply curve of a firm tells us the minimum price at which the firm is willing to supply each quantity. That minimum price is determined by marginal cost: a profit-maximizing firm supplies up to the point where price equals marginal cost ( $P = MC$ ). When a unit tax is imposed—say, $t$ rupees per unit—the firm must pay this tax on every unit it sells, which fundamentally changes the relationship between the market price it receives and the net revenue it keeps.

Suppose before the tax, the firm was willing to supply quantity $Q_1$ at price $P_1$ because at that quantity, $MC = P_1$ . After a unit tax of $t$ is imposed, if the market price remains $P_1$ , the firm receives only $P_1 - t$ per unit (the rest goes to the government). But the marginal cost of producing $Q_1$ is still $P_1$ . Since $P_1 - t < P_1 = MC$ , the firm would now make a loss on the marginal unit and would cut back production. To be willing to supply $Q_1$ again, the firm needs the market price to rise to $P_1 + t$ , so that after paying the tax, it nets $P_1$ —exactly enough to cover marginal cost.

This logic applies to every quantity along the supply curve. For each quantity $Q$ , the price the firm requires from the market increases by exactly $t$ . Graphically, this means the entire supply curve shifts vertically upward by the amount of the tax.

P_{\text{new}} = P_{\text{old}} + t

It is crucial to understand that the supply curve does not shift horizontally or rotate—it undergoes a parallel vertical shift. At any given quantity, the vertical distance between the old and new supply curves is exactly $t$ . The shape and slope of the supply curve remain unchanged; only its position moves up. …

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Q.How does the imposition of a unit tax affect the supply curve of a firm?

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