Question

1.     Suppose the demand for pizza is given by 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 P100 through 150 as the value of pizza

b)     In equilibrium, how many pizzas would be sold and at what price?

c)     What would happen if suppliers set the price of pizza at 50? Explain the market adjustment process.

d)     Suppose the price of hamburgers, a substitute for pizza doubles leading to a doubling of demand for pizzas (at each price consumers demand twice as much pizza as before). Show on a graph.

e)     What is 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   $Qs = 20P-100$

Since the price of P100 through 150 cannot be solved we are assuming the price is P10.0 through 15.0

The demand and supply schedule for pizza using P100 through 150 as the value of P is given below:

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)

If the supplier set the price of Pizza at 50, the demand will be negative which is not possible, hence let's suppose instead the price is 5.0

If the supplier set the price of Pizza at 5

$Qd = 300−20P \\ Qd = 300−20(5) = 300 − 100 = 200\\ Similarly\\ Qs = 20P−100\\ Qs = 20(5)−100 = 100 − 100 = 0$

Thus at price 5.0 the leading to a situation of deficit in the economy.

At this level since the demand is more than the supply, the price will start rising at keep on rising 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.