Shutting down at a price of $4

Work out the loss each way and compare.

If the firm keeps producing 200 units at a price of $4 with ATC of $8, profit is (P - ATC) × Q = (4 - 8) × 200 = -800. It loses $800.

If it shuts down, it earns no revenue and pays no variable cost, but it still owes its fixed cost. Average fixed cost is ATC - AVC = 8 - 5 = 3 dollars per unit, so total fixed cost is 3 × 200 = 600. Shutting down means a loss of $600.

The difference is 800 - 600 = 200, so shutting down saves $200.

The shortcut gives the same number: the price is $1 below AVC, so each unit produced loses $1 on top of the fixed cost, and 1 × 200 = 200. This is why the shutdown rule says to close when price falls below average variable cost.

Each choice

• A. This is the total loss from producing, (4 - 8) × 200. The question asks how much the loss shrinks by shutting down, so that loss still has to be compared with the fixed cost owed either way.
• B. This is the total fixed cost, which is what the firm loses after it shuts down. It is the loss that remains, not the amount saved.
• C. $400 would mean producing costs the firm $2 a unit more than closing, which needs an AVC of $6 at this $4 price. AVC is $5, so the gap is $1 a unit. One way to land on $400 is to subtract total fixed cost from total variable cost ($1,000 minus $600), but that difference compares nothing the owner is choosing between: the choice is a $800 loss from producing against a $600 loss from closing.
• D (correct). Shutting down saves the amount by which price falls short of AVC on every unit, here $1 × 200.
• E. $100 would need a gap of 50 cents a unit over 200 units, or an output of only 100 units. The question fixes AVC at $5, price at $4 and output at 200, so neither holds.