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`