Question

Assume a demand function is given by Qd=40-2P+4Ps-2Pc+5Y and a supply function is given by Qs=16+4P-6Pi, where Ps, Pc, and Pi are the price of a substitute, complement, and input to production respectively. How does a $1 increase in the price of a substitute change the equilibrium price and the equilibrium quantity?

Answer 1

Equilibrium occurs when Quantity demand(Qs) = Quantity supplied(Qs)

Thus Qd = Qs => 40 - 2P + 4Ps - 2Pc + 5Y = 16 + 4P - 6Pi

=> 6P = 40 + 4Ps - 2Pc + 5Y - 16 + 6Pi

=> P = (1/6)(40 + 4Ps - 2Pc + 5Y - 16 + 6Pi)

Now Ps increased by $1 and rest will remain same. Thus we have,

Hence, This means that equilibrium price will increase by 4/6 i.e. $0.67 (approx)

So,Equilibrium Quantity(Q) = Qd = Qs = 16 + 4P - 6Pi

Hence, This means that equilibrium quantity will increase by 16/6 i.e. 2.67 units(approx)

(Note that only Ps changes by 1 and rest are constant. So, and rest of all changes is 0)