Question

D. The market demand and supply for jet fuel is provided by the following functions: Qd = 140 - P Qs = -160 + 4P Where: P= Price per barrel Q= quantity in thousands of barrels If the government imposes a tax of t per unit on quantity supplied and the market adjusts the supply function to include the tax when t = $5/barrel: a. Find the initial equilibrium price and quantity? b. Find the new equilibrium price and quantity after the tax. c. Illustrate with a diagram how this tax will affect the market demand and supply curves. d. Who bears the tax and by how much?

E.. Suppose the airline industry is confronted with a 10% increase in the negotiated wages for their pilots but ticket prices remain constant. Explain with the aid of graphs why the airline might not wish to increase its ticket prices.

Answer 1

(a) Demand function is given as while supply function as . The intital equilibrium price is where quantity demanded is equal to quantity supplied, ie or or or or . Hence, equilibrium price is $60. At this price, quantity demanded is or or and quantity supplied is or or .

(b) Tax rate is fixed as t=$5/barrel, which the government imposes on the supplier. The supply function which was , is adjusted for this, such that now the supplier has to pay t for per unit barrel, hence charge P, but instead of receive P-t only. The new supply function is or or or . Hence, the new equilibrium price is where quantity demanded is equal to the new quantity supplied, ie or or or . At this price, equilibrium quantity demanded is or and or .

(c) The grpah is as below.

Note that the graph is scaled, so that the difference is clearly shown. The effect of tax can be seen as the shift of the supply curve after tax.

(d) The triangle E'DE is the deadweight loss. Tax bear by consumer is area of AE'FB while tax bear by producer is area of BFDC.

Area of AE'FB = , where AE' is new demand quantity which is here 76 units, and AB is difference between equilibrium price before and after the tax is imposed, ie $64 minus $60 or $4. Hence, area of AE'FB = $304.

Area of BFDC = , where BF is new quantity demanded, which is 76 units. BC is difference in equilibrium price before tax, ie $60 and price at which after tax quantity is supplied, ie for , 76 units is supplied at price or . Hence, BC is $60 minus $59, ie $1. Hence, area of BFDC = = $76.

Hence, consumers bear more tax than the producer, by more than $304 - $76 or $228.