Questions: Long-Run Cost Curves and Scale Economies

Question 1

A manufacturing firm is producing 1,000 units per month. Its long-run average cost curve is steeply downward-sloping at this output level. What does this imply about the firm's technology?

• A. The firm is experiencing diseconomies of scale and should reduce output
• B. The firm has constant returns to scale — doubling inputs doubles output
• C. The firm has increasing returns to scale — expanding production would lower per-unit costs
• D. The firm has reached minimum efficient scale and further expansion raises average cost

Answer: (C)

A downward-sloping LAC means average cost falls as output increases — this is the definition of economies of scale, arising from increasing returns to scale. The firm produces each unit more cheaply by expanding. Diseconomies of scale (A) would cause an upward-sloping LAC. Constant returns to scale (B) produce a flat LAC. Minimum efficient scale (D) is the output where LAC reaches its minimum and stops declining — not where it is still steeply falling.

Question 2

Which statement correctly describes the relationship between short-run average cost (SAC) curves and the long-run average cost (LAC) curve?

• A. The LAC is the arithmetic average of all SAC curves at each output level
• B. Each SAC curve lies on or above the LAC, touching it at exactly one point
• C. The LAC coincides with the lowest SAC curve across all output levels
• D. SAC curves shift downward to become the LAC when fixed costs become variable

Answer: (B)

The LAC is the lower envelope of all SAC curves. Because the long run offers full input flexibility — by definition the cost-minimizing option at every output — no SAC curve can lie below it. Each SAC curve corresponds to one specific capital stock; it is tangent to the LAC at the single output level for which that capital stock is optimal. At all other outputs, the fixed capital is suboptimal, making the SAC lie above the LAC. The LAC is not an average of SACs (A), nor does it coincide with any single SAC (C).

Question 3

The minimum efficient scale (MES) is the smallest output level at which a firm reaches its lowest long-run average cost.

• T. True
• F. False

Answer: True

This is the precise definition of MES. It is the output where the LAC curve reaches its minimum and economies of scale are fully exhausted. Below MES, the firm has not captured all available economies of scale and produces at above-minimum average cost. MES also has industry-structure implications: if MES is large relative to total market demand, only a few firms can operate at minimum cost before the market is saturated, predicting concentration.

Question 4

A firm can produce at a point below its long-run average cost curve by optimally adjusting most its inputs.

• T. True
• F. False

Answer: False

This is impossible by construction. The LAC represents the minimum achievable average cost at each output level when all inputs are optimally chosen — it is the lower boundary of feasible average costs. No combination of input choices can yield lower cost than the LAC for any given output; that is what cost minimization means. Points below the LAC are not attainable. Points above it represent suboptimal input choices, as occurs in the short run when some inputs are fixed at non-optimal levels.

Question 5

Explain why each short-run average cost curve is tangent to the long-run average cost curve at exactly one point.

Model answer: Each SAC curve is constructed for a specific capital stock K₀. At exactly one output level q₀, the capital K₀ is precisely optimal — the cost-minimizing amount for producing q₀. At that point, the firm is at its long-run optimum given this capital, so the SAC and LAC agree and are tangent. At any other output level, K₀ is either too much or too little capital, making production more expensive than it would be with flexibly chosen capital — so the SAC lies strictly above the LAC. The LAC stitches together one optimal point from each possible SAC into a smooth envelope.

This envelope relationship is not a coincidence — it is the mathematical definition of the LAC. Every point on the LAC is a tangency with some SAC, each representing the long-run optimum for a different capital level and its associated output quantity.