Question

Questions 16 to 22 The demand and supply for good x are respectively QD = 28 – Px + Py/2 and QS = Px – 10 with QD denoting the quantity demanded for good x, QS the quantity supplied for good x, Px the price for good x, and Py the price for good y a substitute to good x. Suppose Py = 4. 16) Determine the cross-price elasticity of demand at the equilibrium. Suppose the government imposes a unit tax of 10 on producers. 17) Determine the price paid by consumers. 18) Determine the quantity purchased and supplied. 19) Determine the size of the tax supported by consumers (not the share of the government’s tax revenues supported by consumers). 20) Determine the price received by producers. 21) Determine the size of the tax supported by producers (not the share of the government’s tax revenues supported by producers). 22) Determine the deadweight loss due to the tax.

Answer 1

At equilibrium Qd=Qs

28-Px+4/2=Px-10

Px=20

Qd=10=Qs

16. Cross price elasticity =dQd/dPy *Py/Qd=1/2*4/10=.2

17.Qs=(Px-10)-10=Px-20 (since supply will decrease by imposing of tax)

Therefore, new equilibrium price is

28-Px+2=Px-20

Px=25(Price paid by consumers)

18.Qd=Qs=25-20=5

19. Size of tax supported by consumers=Increase in price paid by consumers*Quantity=(25-20)*5=25

20.Price received by producers=25-10=15

21.Size of tax paid by producers=(Decrease in price paid by producers)*Q=(20-15)*5=25

22. Deadweight loss due to tax=1/2*10*(10-5)=25 (Triangle ABC is deadweight loss)