Study the diagram below carefully and use the given information to answer the questions that follow: (a) Determine: (i) the profit maximizing output; (ii) t...

The diagram shows a firm in perfect competition. The marginal revenue line MR is horizontal at \(\$10\), so price \(P = MR = \$10\). The average total cost curve ATC is U-shaped with its minimum of \(\$6\) at an output of \(600\) units, and it reads \(\$8\) at \(400\) units. The rising marginal cost curve MC cuts the MR line at \(900\) units. These read-off values drive the working below.

(a)(i) Profit-maximising output

A firm maximises profit where marginal cost equals marginal revenue while MC is rising. On the diagram MC cuts MR at:

\[MC = MR = \$10 \ \Rightarrow\ Q = \mathbf{900\ \text{units}}\]

(a)(ii) Profit if the firm produces 600 units

At \(600\) units, \(ATC = \$6\) (the lowest point of the ATC curve) and \(P = \$10\).

\[TR = P \times Q = 10 \times 600 = \$6{,}000\]\[TC = ATC \times Q = 6 \times 600 = \$3{,}600\]\[\text{Profit} = 6{,}000 - 3{,}600 = \mathbf{\$2{,}400}\]

(a)(iii) Total cost if the firm produces 400 units

At \(400\) units the ATC curve reads \(\$8\):

\[TC = ATC \times Q = 8 \times 400 = \mathbf{\$3{,}200}\]

(b)(i) Total revenue at 900 units

\[TR = P \times Q = 10 \times 900 = \mathbf{\$9{,}000}\]

(b)(ii) Profit at 900 units

Reading the ATC curve at the profit-maximising output of \(900\) units gives approximately \(ATC \approx \$8\):

\[TC = ATC \times Q = 8 \times 900 = \$7{,}200\]\[\text{Profit} = TR - TC = 9{,}000 - 7{,}200 = \mathbf{\$1{,}800}\]

(c) What happens if market price falls below average variable cost

If price falls below average variable cost, the firm cannot even cover the running (variable) costs of producing. Every unit sold would then add to its losses on top of the fixed costs it must pay anyway. The sensible decision is to shut down (cease production) in the short run: by producing nothing the firm loses only its fixed cost, which is smaller than the loss it would make by continuing. The point where \(P = \text{minimum } AVC\) is therefore called the shut-down point.