Question

Suppose that the demand and supply for milk for Furi dairy farm is given by

where the quantity is in liters and the price is in birr per liter. Assume there is no import or export of milk.

A) Find the market equilibrium quantity, and the equilibrium price.

B) Find the consumer and producer surplus at the market equilibrium that you found in part (a).

C) Assume now that there is a price floor of 36 birr per liter. What is the new quantity sold in the market?

Answer 1

Let's take the Quantity Demand and Quantity Supply functions which are in terms of P to be

$\displaystyle\\Qd=100-5p, Qs=-125+20p$

(a) We shall then find the equilibtium quantity and equilibrium price

To get the equilibrium price P, we set the Quantities to each other. That is,

We set, $\displaystyle\\Qd=Qs$

We then have,

$\displaystyle\\100-5p=-125+20p\\collecting \hspace{0.2cm}like\hspace{0.2cm}terms\\100+125=20p+5p\\225=25p\\p=\frac{225}{25}\\p=9\\which\hspace{0.1cm}is\hspace{0.1cm}the\hspace{0.1cm} equilibrium \hspace{0.1cm}price$

Also,

To get the Equilibrium quantity

We plug $P=9$ in either of the $Qs$ or $Qd$ as they both would arrive at the same result.

Set $P=9$ in $Qd$

$\displaystyle\\Qd=100-5p\\\hspace{0.56cm}=100-5(9)\\\hspace{0.56cm}=100-45\\\hspace{0.56cm}=55$

Also, we'll check for $Qs$

$Qs=-125+20p$

$=-125+20(9)\\=-125+180\\=55$

Therefore, the market equilibrium quantity and equilibrium price are 55 and 9 respectively.

(b) To get the consumer and producer surplus at the market equilibrium, We use the graph

Which shows the demand and supply curve.

The Consumer surplus is calculated by the Area of the topmost blue coloured triangle in the diagram with $base=55, height=6$

$\displaystyle\\A=\frac{1}{2}( base \hspace{0.1cm}*\hspace{0.1cm}height\\$

$\displaystyle\\A=\frac{1}{2}(55*6)$

$A=165$

Also,

The producer surplus is given by the Area of the red colored triangle with $base=7, height=55$

$\displaystyle\\A=\frac{1}{2}( base \hspace{0.1cm}*\hspace{0.1cm}height)\\$

$\displaystyle\\A=\frac{1}{2}(55*7)$

$A=\frac{385}{2}\\A=192.5$

HENCE, the consumer and producer surplus are $165\hspace{0.1cm}and\hspace{0.1cm}192.5\hspace{0.1cm} respectively$

(c) To get the quantity sold in the market assuming price floor of $36 \hspace{0.1cm}birr/ltr$

We shall plug $P=36$ in $Qs$

$Qs=-125+20p$

$=-125+20(36)\\=-125+720\\=595$

Which gives the quantity sold.