I'm not sure which formula I should apply to these practice questions, could you please explain?

Suppose the marginal control costs (MC) and the total costs (TC) of reducing emissions for two steel producers are:

Producer 1:

MC₁= 10Q₁

TC₁= 5(Q₁)²

Producer 2:

MC₂= 40Q₂

TC₂= 20(Q₂)²

Where MC₁and MC₂are the marginal control costs and Q₁and Q₂are the volumes of emissions reduced by Producers 1 and 2 respectively. With no controls at all, each firm emits 50 units totalling 100 units.

a. Suppose the government allocates emissions reductions equally among the two producers to reduce total emission by half (that is each firm has to reduce emissions by 25 units). Calculate the total cost to each firm (Hint: use the total cost function TC).

b. Calculate the cost-effective allocation of control responsibility if a total reduction of 50 emission units is required. What is the total control cost and how does this compare to part a?

c. If the government wants to charge an emission tax, what per unit tax should they impose?

d. How much total revenue would the Government collect from the emission tax in part b

e. If instead the government used a cap and trade scheme and, based on histrocial emissions, allocated 25 units to each firm. What is the pattern of trade expected? What is the equilibrium price of permits?