Question

3. Suppose the market demand for pizza is Qd = 300-20P and the market supply for pizza is given by Qs = 20P - 100 where P = price per pizza.
a) Graph the supply and demand schedules for pizza using P5 through P15 as the value of P.
b) In equilibrium, how many pizzas would be sold and at what price?
c) What would happen if suppliers set the price for pizza at 15? Explain the market adjustment process.
d) Suppose the price of hamburgers a substitute for pizza doubles. This leads to a doubling of the demand for pizza (at each price consumers demand twice as much pizza as before). Write the equation for the market demand for pizza.
e) Find the new equilibrium price and quantity of pizza

Answer 1

a) Given that,

Market demand for pizza $Q d = 300−20P$

Market supply for pizza   $Qs = 20P-100$

Graphical presentation of the equilibrium price 

b)

$Qd=Qs\\300-20p=20p-100\\300+100=20p+20p\\P=10\\Q=300-20(10)\\Q=100$

c)

$Qd = 300−20P \\ Qd = 300−20(15) = 300 − 300 = 0\\ Similarly\\ Qs = 20P−100\\ Qs = 20(15)−100 = 300 − 100 = 200$

Thus at price 15.0 the leading to a situation of surplus in the economy.

At this level since the demand is less than the supply, the price will start falling until the $Qd = Qs.$

d)

Suppose the price of the hamburgers, a substitute for pizza doubles, This leads to a doubling of the demand for pizza. Thus, the new market demand will be twice the old demand i.e $Qd' = 2Qd.$

$Qd' = 2(300-2P)\\ = 600 - 40P$

e)

$Qd' = Qs$

$600 - 40P = 20P - 100 \\ 60P = 700,\\ P = 11.67 ≈12\\ Qd' = 600 - 40P \\= 600 - 40(11.67) \\= 600 - 466.8 \\ = 133.2 ≈ 133$

Thus the new equilirbum price is approx 12 whereas the new equilibrium quantity is 133.