1st Assignment of ECO -401 Fall 2010

Question:

Suppose the market demand and market supply for coffee is given by the
following equations:
Qd = 850 – 15P
Qs = 400 + 30P

A.Find quantity demanded and quantity supplied when the price of coffee is
Rs. 8. Is there a surplus or shortage in the production of coffee? What
should happen to the price of coffee?

B. Find the equilibrium price for coffee by using given demand and supply
equations.

C. Prove that the price found in part (B) is an equilibrium price.

D. Show the equilibrium condition in coffee market graphically.
Marks: A = 6(4+1+1), B = 2, C = 3, D = 4

Solution of Assignment
Solution Part A:
Quantity demanded is found by letting P equal to Rs. 8 in the demand equation.
Thus,
Qd = 850 – 15P
= 850 – 15(8)
= 850 – 120
= 730
Similarly,
Qs = 400 + 30P
= 400 + 30(8)
= 400 + 240
= 640
There is a shortage of production since 730 units are demanded and 640 units
are supplied when the price per unit is Rs. 8. There is therefore upward
pressure on the Rs. 8 price for coffee.

Solution Part B:
The equilibrium price for coffee is found by equating Qd and Qs.
Qd = Qs
850 – 15P = 400+30P
30P + 15P = 850 – 400
45P = 450
P = 10

Solution Part C:
At equilibrium, the quantity demanded must equal the quantity supplied.
Substituting the Rs.10 equilibrium price into the market demand and market
supply equations:
Qs = 400 +30P Qd = 850 – 15P
= 400 + 30(10) = 850 – 15 (10)
= 400 + 300 = 850 - 150
= 700 = 700
We find that quantity demanded and quantity supplied each equals 700 units.