# Demand & Supply, Solved Questions

#### 1- Solved Questions

1- Given that: Qd/1500 + P/1500 = 1 and Qs = 4P, what is quantity supply or quantity demanded?

Solution-1;
Given the demand function,
\frac{Qd}{1500}+\frac{P}{1500}=1
\Or,\frac{Qd+P}{1500}\=1
\Or,\Qd\=\1500-P.......(i)

Given the supply function Qs = 4P.....(ii)
For equilibrium, Qd must be equal to Qs,
Or, Qd = Qs .......(iii)
Substituting the demand and supply functions in equation (iii) we get,

1500 - P = 4P
Or,1500=4P+P
Or,1500=5P
\Or,\frac{1500}{5}\=P
Hence P = 300

Substituting 300 for P in demand or supply function we get,
Qs=4×300
Qs=1200
if you substitute in the demand function you get,
Qd=1500-300
Qd=1200
Hence, Qd or Qs is equal to 12oo.

2- If the quantity demanded of a commodity reduces from 20 units to 10 units in response to an increase in price from $10 to$20, what is the coefficient of price elasticity?

Solution-2;
Given, \P1=10\&\P2=20
\Q1=20\&\Q2=10
\triangleP=P2-P1\and\triangleQ=Q2-Q1
\triangleP=20-10\and\triangleQ=10-20
\triangleP=10\and\triangle\Q=-10
As we know that price elasticity demand is,
\ep=\-\frac{\triangleQ}{\triangleP}\times\frac{P}{Q}
\ep=\-\frac{-10}{10}\times\frac{10}{20}
\ep=\frac{1}{2}
\ep=0.5

3- Given the demand function Q=-110P+0.32I, where P is the price of the good and I is the consumer's income. What is the income elasticity of demand when income is 20,000 and the price is $5? Solution-3; As we know that income elasticity of demand is; \eI=\frac{\triangleQ}{\triangleI}\times\frac{I}{Q} In the above problem, initial income and quantity are not given. Hence, \eI=\frac{\triangleQ}{\triangleI} can be calculated by differentiation method. Note:- Income elasticity of demand states the responsiveness in quantity demanded of a good due to a change in income of consumers. Hence, P in the above demand function can be substituted by$5, and the demand function changes to;

Q=-110×5+0.32I
Q=-550+0.32I
Differentiating both sides with respect to I we get;
\frac{dQ}{dI}=\frac{dQ(-550+0.32I)}{dI}
\frac{dQ}{dI}=0.32

Now, let us assume, initial quantity is: Q=-550+0.32I
Initial income is: 20,000
\frac{△Q}{△I}=0.32

Now, let us plot the value in the following formula.
\eI=\frac{\triangleQ}{\triangleI}\times\frac{I}{Q}

Hence,\eI=0.32\times\frac{20,000}{-550+0.32I}
\eI=0.32\times\frac{20,000}{-550+0.32(20,000)}
\eI=\frac{6,400}{-550+6,400}
\eI=\frac{6,400}{-550+6,400}
\eI=\frac{6,400}{5,850}
\eI=\frac{6,400}{-550+6,400}
\eI=1.09

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