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 



A

(1)

P=8

Q(d)=850-15(p)

Q(s)=400+30(p)

Put price in q(d) and q(s)

Q(d) Q(s)

=850-15(p) =400+30(P)

=850-15(8) =400+30(8)

=850-120 =400+240

=730 =640

(2)

shortage production because Q(d) is high and Q(s)low is low eight is not equilibrium price

(3) Shortage will increase price



(B)

Equilibrium price

Q(d)=Q(s)

850-15(p)=400+30(p)

45p=450

p=450/45

p=10

Equilibrium price =10

Here demand and supply is equal



(C)

Equilibrium proved

Q(d)=Q(s)

850-15(p)=400+30(p)

850-15(10)=400+30(10)

850-150=400+300

700=700

(D)

Graphical 

...............


A. Calculation of quantity demand and quantity supply

The given equations are
1. Q (d) =850-15(p)
2. Q(s) =400+30(p)
As we know that the given price of coffee is P = 8 Rs.
So, to find out the quantity demand and quantity supply put the value of price P in above equations.
So, Put price in q (d) and q(s)

Q (d) =850-15(p) Q(s) =400+30(p)

Q (d) =850-15(8) Q(s) =400+30(8)
Q (d) =850-120 Q(s) =400+240
Q (d) =730 Q (s) =640

(a) From the above results, we have to know that this is a
Shortage production of coffee because Q (d) is high and Q(s) is low so, eight (8) is not equilibrium price

(b) If there will be a shortage of production that is, Q (d) will be high and Q (s) will be low, then this shortage of that production will increase price.

B. Calculation of equilibrium price by using above equations

As we know that if Q (d) will be equal to Q(s) the price will be equilibrium
So,

Q (d) =Q(s)
850-15(p) =400+30(p)
850-400=30(p) +15(p)
450=45(p)
p=450/45
p=10 Rs.

So, Equilibrium price =10
Here demand and supply is equal

C. Equilibrium proved

By putting the value of equilibrium price in Q (d) and Q (s) we can prove it.
So,
Q (d) =Q(s)
850-15(p) =400+30(p)
850-15(10) =400+30(10)
850-150=400+300
700=700

Thus proved if p=10 then Q (d) and Q (s) will be equal




D. The graph with the help of table.


Price Quality demand Quality supply
9 715 670
10 700 700
11 685 730
......................

QUESTION NO 1 (A)

(1)
P=8
Q(d)=850-15(p)
Q(s)=400+30(p)
Put price in q(d) and q(s)
Q(d) Q(s)
=850-15(p) =400+30(P)
=850-15(8) =400+30(8)
=850-120 =400+240
=730 =640
(2)
shortage production because Q(d) is high and Q(s)low is low eight is not equilibrium price
(3) Shortage will increase price

(B)
Equilibrium price
Q(d)=Q(s)
850-15(p)=400+30(p)
45p=450
p=450/45
p=10
Equilibrium price =10
Here demand and supply is equal

(C)
Equilibrium proved
Q(d)=Q(s)
850-15(p)=400+30(p)
850-15(10)=400+30(10)
850-150=400+300
700=700

(D)

Graphical
Price Quality demand Quality supply
9 730 640
10 700 700
11 685 730