A Question asked in IES Exam 2014.

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A Question asked in IES Exam 2014.

E A Ibrahim
Consider a manufactured good whose production process generates pollution. The annual demand for the good is given by Qd = 100-3P. The annual market supply is given by Qs=P. In both equations, P is the price in rupees per unit. For every unit of output produced the industry emits one unit of pollution. The marginal damage from each unit of pollution is given by 2Q.
(a) Find the equilibrium price and quantity in a market with no government intervention.
(b) Find the socially optimal quantity of the good. What is the socially optimal market price?

I am getting the answer of first question as P=25 and Q=25. Please help with the second.