Thermal Inc. (TI) is considering two possible locations for a new coal-fired power plant: one adjacent to Mine 1 and the other adjacent to Mine 2, which are 100 km apart.
The marginal cost (MC) of production is $3 per ton for Mine 1 and $5 per ton for Mine 2.

TI can purchase coal from either mine, but the transportation cost is $2 per ton per 100 km.

Suppose TI locates its plant next to Mine 1 (perhaps by mistake) and invests heavily in infrastructure there (a sunk cost).
What is the likely Bertrand price in whole number that Mine 1 would charge TI, assuming TI pays the one-way transportation cost, if any, for coal?

(Note: The price refers to the one charged by the mines, which may be influenced by transportation costs.)

Question

Thermal Inc. (TI) is considering two possible locations for a new coal-fired power plant: one adjacent to Mine 1 and the other adjacent to Mine 2, which are 100 km apart.
The marginal cost (MC) of production is $3 per ton for Mine 1 and $5 per ton for Mine 2.

TI can purchase coal from either mine, but the transportation cost is $2 per ton per 100 km.

Suppose TI locates its plant next to Mine 1 (perhaps by mistake) and invests heavily in infrastructure there (a sunk cost).
What is the likely Bertrand price in whole number that Mine 1 would charge TI, assuming TI pays the one-way transportation cost, if any, for coal?

(Note: The price refers to the one charged by the mines, which may be influenced by transportation costs.)

BlackTom AI · Accepted Answer

The problem describes two coal mines that TI can source from, with different marginal costs and a fixed transportation arrangement. Here is a step-by-step way to think about it and why the number 6 emerges as the Bertrand price in this setup.

- First, establish the delivered cost from each mine to TI’s plant when TI pays the transportation cost. Since the plant is located next to Mine 1, the distance from Mine 1 to the plant is effectively 0 km, so the transportation cost for coal from Mine 1 is zero. The delivered cost from Mine 1 to TI is therefore simply its marginal cost: MC1 = 3 per ton.

- For Mine 2, the plant is 100 km away, so the transportation cost is 2 per ton (per 100 km). The delivered cost from Mine 2 to TI is its marginal cost plus the transport: Delivered from Mine 2 = MC2 + transport = 5 + 2 = 7 per ton.

- In a Bertrand-style price competition, TI will choose the supplier with the lower delivered price, since the two mines offer an essentially homogeneous good (coal) delivered to the same plant. Therefore, Mine 1 would like to set its price so that the delivered price from Mine 1 remains at or below the delivered price from Mine 2.

- The critical comparison is between Mine 1’s price (P1) and Mine 2’s delivered price. If Mine 1 charges P1, TI will compare P1 (from Mine 1, since transport cost is 0) with 7 (the delivered cost from Mine 2, assuming Mine 2 charges its marginal cost of 5 plus the 2 transport). TI will buy from Mine 1 as long as P1 ≤ 7. To ensure Mine 1 captures the entire demand (and prevent TI from switching to Mine 2), Mine 1 would price as high as possible without becoming more expensive than Mine 2’s delivered alternative.

- However, because this is a Bertrand setting, Mine 2 could respond by adjusting its price, but its minimum viable price is constrained by its own marginal cost. Its delivered price cannot fall below 7 (since MC2 = 5 and transport is 2, total 7). Therefore, as long as Mine 1 can price at or below 7, TI will favor Mine 1’s offer.

- To determine a specific whole-number price that Mine 1 would charge, we consider the need to undercut the alternative’s delivered price just enough to ensure TI prefers Mine 1, while also recognizing that Mine 2 cannot credibly threaten a lower delivered price than 7. The highest price Mine 1 can set while still keeping TI with Mine 1 (given the alternative is 7) is just below 7. Since prices are asked in whole dollars, the largestWhole-number price that remains competitive relative to Mine 2’s 7-delivered-cost benchmark is 6.

- Therefore, the likely Bertrand price Mine 1 would charge TI, in whole dollars, is 6 per ton. This price keeps Mine 1’s delivered price at 6 (since transport from Mine 1 is zero) and remains below Mine 2’s delivered cost of 7, ensuring TI continues to buy from Mine 1 rather than Mine 2. The sunk-cost aspect of investing in Mine 1’s location affects strategic posture and incentives but does not raise Mine 1’s delivered price above 6 in this competitive setup.

Note: There are no answer options provided in this question. The reasoning above leads to the conclusion that Mine 1’s Bertrand price to TI, under the stated assumptions and with TI paying the transportation cost as described, would be 6.

COMM_V 295 105 106 2025W1 Participation/Math Quiz #2

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