Carbon Price Fuel Switching

Under a cap-and-trade scheme every tonne of CO2 emitted must be covered by an allowance, so the carbon price $C$ (dollars per tonne) is added to a plant's cost per MWh of electricity.

• A coal plant has a fuel and variable cost of 30 dollars per MWh and emits 0.95 tonnes of CO2 per MWh.
• A gas plant (combined cycle) has a fuel and variable cost of 50 dollars per MWh and emits 0.37 tonnes of CO2 per MWh.

Dispatch is in order of total marginal cost, cheapest first. At what carbon price $C$ (dollars per tonne) do the two plants have equal all-in marginal cost, so that any higher price makes gas dispatch ahead of coal? Give an exact fraction or a decimal to at least 6 significant figures.