Question

For all graphs, be sure to correctly and completely label all axes and curves and use arrows to indicate the direction of any shifts.

Assume that the market for tea is in equilibrium.

1. Graph the market for tea, assuming unit-elastic supply and demand. Label the equilibrium price Pe and the equilibrium quantity Qe.
2. The price of coffee increases from $5 to $6, and the quantity demanded of tea increases from 40 thousand units to 50,000 units. What is the cross-price elasticity of tea and coffee?
3. Are coffee and tea substitutes or complements? Explain using the elasticity coefficient.
4. Illustrate the effect of the change in the market for coffee from part (b) on your market graph for tea from part (a), labeling the new equilibrium price and quantity Pe2 and Qe2, respectively.
5. What happened to the producer surplus in the market for tea as a result of part (d)?
6. On a new graph, illustrate the effect of an effective price ceiling on coffee. Label the price ceiling Pc, and the quantity exchanged with the ceiling Qc.
7. Shade the deadweight loss from the price ceiling.
8. The pre-ceiling equilibrium price was $4, the price ceiling is $3, and the quantity consumed went from 200 thousand units to 150 thousand units. What is the total amount of revenue lost because of the price ceiling?

Answer 1

Price of coffee, Pc = $5
Price of coffee increases to, P'c = $6

Quantity demanded of tea, Q = 40000
Quantity demanded of tea increases to, Q' = 50000

The cross price elasticity of demand is the ratio of percentage change in quantity demanded and the percenatge change in price of related good.

E = %Qe / %Pc

%Qe =

=

= 10000/45000 * 100

%Qe = 22.22

%Pc =

=

= 1/5.5 * 100

%Pc = 18.18

E = 22.22 / 18.18

E = 1.22

As we can see that cross price elasticity is 1.22 which is greater than 1, it means that quantity demanded of tea increases more when price of tea increases. Therefore, tea and coffee are substitutes goods.

As price of coffee increases, the quantity demanded of tea increases. The demand curve shifts to rightwards from D to D'. As a result the equilibrium price increases to Pe2 and equilibrium quantity also increases to Qe2.

Producer surplus is the surplus generated by the producers as a difference between what they are willing to accept and what they actually get for a product. As price of tea increases to Pe2 and demand curve shifts rightwards, the producer surplus which is the area between the supply curve and the price line increases.

Price of coffee, P = $4
Quantity, Q = 200000

Price ceiling of $3 is imposed in the market for coffee. As a result the quantity exchanged falls down to 150000.

The deadweight loss arises in the market when there is inefficiency. The deadweight loss due to a price ceiling will be the yellow coloured area in the above figure.

Before price ceiling:

The revenue earned by producers before price ceiling was;

TR = P*Q
= 4 * 200000
TR = 800000

After price ceiling:

The revenue earned by producers after price ceiling is;

TR' = Pc*Q
= 3 * 150000
TR' = 450000

Therefore, the loss in total revenue is;

Loss = TR - TR'
= 800000 - 450000

Loss = 350000