Condition 3

This figure is the short-run shutdown diagram. It is a single plot with the market price $p$ on the vertical axis and the firm’s output $q$ on the horizontal axis. Three curves are drawn: the firm’s short-run marginal cost curve ($SMC$), its short-run average cost curve ($SAC$), and its average variable cost curve ($AVC$). The $AVC$ curve is U-shaped, and its lowest point is the minimum of $AVC$. A horizontal line at price $p$ is drawn across the diagram. The key feature is that this price line lies below the minimum point of the $AVC$ curve — meaning the price is too low to cover even the variable cost per unit at any output level.

The physical idea is brutally simple: if the price does not cover the average variable cost at any output, every unit the firm produces adds more to cost than to revenue. Producing anything would make the loss larger than the loss from shutting down. The profit-maximising (or loss-minimising) choice in the short run is therefore to produce zero output. The firm shuts down.

The textbook uses this figure to derive the shutdown condition. For any output $q$, the firm’s profit is $\pi(q) = pq - TC(q)$, where $TC(q) = TFC + TVC(q)$. If the firm produces nothing, revenue is zero and total cost equals total fixed cost $TFC$, so the loss is exactly $TFC$. If the firm produces some $q > 0$, the loss is $TFC + TVC(q) - pq$. The firm is better off producing zero whenever the loss from producing is larger than $TFC$, i.e. whenever $TVC(q) - pq > 0$, or equivalently $pq < TVC(q)$. Dividing by $q$ gives the condition:

If the market price is less than the average variable cost at every possible output, the firm produces nothing. The shutdown point is the minimum of the $AVC$ curve: the firm produces zero whenever $p$ is below that minimum.

The figure also illustrates the loss from producing at a specific output $q_1$ when $p$ is below $AVC$. At $q_1$, total variable cost is $AVC(q_1) \times q_1$, which is the area of a rectangle with height $AVC(q_1)$ and width $q_1$. Total revenue is $p \times q_1$, a rectangle of height $p$ and width $q_1$. The difference — the amount by which variable cost exceeds revenue — is the rectangle with height $AVC(q_1) - p$ and width $q_1$. In the figure, this rectangle is labelled with vertices $p$, $E$, $B$, $A$ (where $p$ and $E$ lie on the vertical axis — $E$ at the height of $AVC(q_1)$ — while $B$ lies on the $AVC$ curve at output $q_1$ and $A$ lies on the price line at $q_1$). The area of rectangle $pEBA$ equals $[AVC(q_1) - p] \times q_1$, which is exactly the extra loss beyond fixed cost that the firm would incur if it foolishly produced $q_1$ instead of shutting down.

The figure plots the long-run average cost (LRAC) and long-run marginal cost (LRMC) curves of a firm against the market price, with quantity on the horizontal axis and cost/revenue per unit on the vertical axis. The LRAC curve is U-shaped, showing that average cost first falls as output increases (economies of scale), reaches a minimum point, and then rises (diseconomies of scale). A horizontal line is drawn at the market price $p$, which is less than the minimum point of the LRAC curve. The firm’s profit-maximising output in the short run would be where marginal cost equals price, but in the long run the firm cannot cover its average costs at any positive output level.

The key physical idea is that in the long run, a firm under perfect competition must earn at least zero economic profit to stay in the market. If the market price falls below the minimum of the LRAC curve, the firm cannot produce any positive output without making a loss. The figure shows this situation: at the output level $q_1$, the firm’s average cost is higher than the price. The total cost of producing $q_1$ units is the rectangle with height equal to the average cost at $q_1$ and width $q_1$, while total revenue is the rectangle with height $p$ and width $q_1$. The difference — the loss — is the rectangle labelled $pEBA$ in the textbook. Because the price is below the minimum LRAC, the firm’s best decision is to produce zero output in the long run, shutting down entirely.

The textbook uses this figure to derive the condition for long-run equilibrium of a firm under perfect competition. The central result is that in long-run equilibrium, the firm produces at the minimum point of its LRAC curve, where price equals both marginal cost and average cost. The formula for zero economic profit is:

Here, $p$ is the market price (which the firm takes as given), $\text{LRMC}$ is long-run marginal cost, and $\text{minimum LRAC}$ is the lowest point on the long-run average cost curve. At this point, total revenue equals total cost, so economic profit is zero. The figure with price below minimum LRAC shows the opposite case — the firm cannot achieve this condition and must exit the industry. …