Question

Suppose the demand for a particular textbook, as a function of price, is given by Q Demanded (P)=60-P, and
supply as a function of price is Q Supplied (P)=P.
(a) What is the equilibrium price and quantity in this market?
(b) Sketch the supply and demand curves on the same graph.
(c) If the price were fixed at P=10 is there a excess supply or excess demand of textbooks, and by
how much?
(d) In equilibrium, what is the producer surplus? Consumer surplus? Total surplus?
(e) Suppose one more buyers arrive. She says “I will pay any amount for up 20 textbooks” Also,
all buyers who are willing to pay $10 or less (such as Bob, who is willing to pay $7, who was
part of original Q D (P)=60-P demand curve) find free alternatives and thus no longer want a
textbook, regardless of price. Assuming we believe all of this, sketch the new demand curve as
precisely as possible.

I am primarily concerned with e.

Answer 1

We have the demand for a particular textbook, Q Demanded (P)=60-P, and supply as a function of price is Q

Supplied (P)=P.

(a) This is done by equating demand and supply

60 - P = P

60 = 2P

P* = 30 and Q = 60 - 30 = 30 units. Equilibrium price is $30 and quantity is 30 units

(b) Below is the grpah showing supply and demand curves.

(c) If the price were fixed at P=10 Demand is Qd = 60 - 10 = 50 units and supply is Q = 10. Hence there is an excess demand of textbooks by 50 - 10 = 40 units.

(d) In equilibrium, what is the producer surplus? Consumer surplus? Total surplus?

CS is the area of region below the demand curve and above the price line. CS = 0.5*(60 - 30)*30 = $450. PS is the area of theregion below the price line and above the supply curve. PS = 0.5*(30 - 0)*30 = $450. Total surplus = TS = PS + CS = $900.

(e) Suppose one more buyer arrive. She says “I will pay any amount for up 20 textbooks” Also, all buyers who are willing to pay $10 or less (such as Bob, who is willing to pay $7, who was part of original Q D (P)=60-P demand curve) find free alternatives and thus no longer want a textbook, regardless of price.

So there are two buyers, one with perfectly inelastic demand (fixed at 20 books) and a group who face a demand curve Q = 0 for a price below $10. Hence the new demand curve has the following construction

• From price 0 to 10, quantity demanded is 0 from original demand, and 20 textbooks from new buyer. Hence demand is vertical from 0 to 9 but fixed at 20 units.
• When price is increased beyond 10, original demand function is 60 - P. But the new buyer is paying any amount for 20 units. Hence demand curve is shifted up by 20 units at all price levels till 60.
• When price is 60 or more, there is no quantity demanded in old function. But the new buyer can pay anything for 20 units. Hence demand again becomes vertical at Q = 20