12. In a competitive market the (inverse) demand function is given by

P = 10 Q

where P denotes price and Q denotes market quantity. There are 10 identical firms in the market and the cost of the representative firm producing q units of output is given by

C(q) = 2q + 5q²

Firms are price takers.

(a) Derive the market supply function.

Parts (b) and (c) ask you to calculate values of deadweight loss. You should also show the loss on a diagram in each case. If your calculations are incorrect you will still receive a part of the allocated marks if the diagram shows the right areas for the loss

(b) Suppose the government imposes a price-ceiling of P = 4. Calculate the deadweight loss under the usual assumption that the quantity supplied at the ceiling price is obtained by the consumers who value the good the most (i.e. denoting the market quantity supplied under the ceiling by Q_C, the supply is obtained by consumers with values between 10 and 10 Q_C).

(c) For the policy introduced in part (b), calculate the deadweight loss under the most pessimistic scenario in which the quantity supplied at the ceiling price is obtained by the consumers who value the good the least (i.e. denoting the market demand at the ceiling price by Q_D, the supply is obtained by consumers with values between 10 (Q_D Q_C) and 10 Q_D).