1. Hello,

I am kinda stuck with is a particular question. Please, any insights??
The question is on competitive firm and emission tax
Consider a competitive firm, which produces product y and releases emissions amounting to 40 % of produced amount (Ey=0.4y). The price of the product is p = 10. The costs of production and abatement (a) are defined by c(y,a) = 0.5y2 + 0.02ya + 0.5a2. Authorities levy a tax, t = 2 on each unit of emissions released to the nature. Calculate how much the firm produces and abates in the presence of the emission tax. Suppose that the society uses a quantity constraint on emissions that is set equal to the amount of emissions that the firm releases under the tax. Show that the value of the Lagrange multiplier l is equal to the tax rate but the profits of the firm are higher than in the presence of the emission tax.

2.

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