Firms and production — practice questions

(a) MC = ΔTC/ΔQ:

(b) Profit max where MC = MR = £12: At Q = 4, MC = £12 = MR ✓

TR = 12 × 4 = £48 TC = £54

Wait — at Q = 4, TC > TR. Check Q = 3: MC = 8 < MR → should expand. At Q = 4: MC = 12 = MR → optimal output = 4 units.

Profit = TR − TC = 48 − 54 = −£6 (loss).

The firm maximises profit (minimises loss) at Q = 4. In the short run, it continues if TR ≥ TVC. TFC = £20, TVC at Q=4 = £34, TR = £48 > TVC → covers variable costs, so it should stay open short run.

Step 1: Recall the cost formulas.

• TC = TFC + TVC
• AFC = TFC / Q
• AVC = TVC / Q
• AC = TC / Q (or AFC + AVC)
• MC = ΔTC / ΔQ

Step 2: Calculate TC for each output level.

• Q=1: TC = $50 +$30 = $80$
• Q=2: TC = $50 +$50 = $100$
• Q=3: TC = $50 +$65 = $115$
• Q=4: TC = $50 +$90 = $140$
• Q=5: TC = $50 +$130 = $180$

Step 3: Calculate AFC, AVC, AC, and MC for each output level and tabulate the results.

| Q | TFC ($) | TVC ($) | TC ($) | AFC ($) | AVC ($) | AC ($) | MC ($) |$ |---|---|---|---|---|---|---|---|

Note: MC is the change in TC from the previous unit. For Q=1, MC = $80 -$50 = $30. For Q=2, MC =$100 - $80 =$20, and so on.