Are quantities supplied-demanded equal in intervation

Question

In perfectly competitive market, the market demand curve is given by Q^d = 10 − P^d, and the market supply curve is given by Q^s = 1.5P^s.

a) Prove that the market equilibrium price and quantity in the lack of government intervention are of P^d = P^s = 4 and Q^d = Q^s = 6.

b) Let’s take two possible govt. interventions: (i) The price ceiling of $1 per unit; (ii) The subsidy of $5 per unit remunerated to producers. Prove that the equilibrium market price paid by consumers beneath the subsidy equivalents $1, the similar as the price ceiling. Are the quantities supplied and demanded similar beneath all government intervention?

Answer 1

a)    10 – P = 1.5P => P = 4 and Q = 10 – 4 = 6.

b) Beneath $5 subsidy remunerated to the producer, market price P = Pd and the after-subsidy price obtained by producers is P^s = P^d+5. Therefore: 10 – P = 1.5(P + 5) => P = 1.