Question

(ii)  Suppose the demand equation for good Y is given as Q = 50–2.5P where Q is the quantity demanded and P is the price. What price would the monopolist set if he had 50 units? How many would he sell? What price would he set if he had 100units? How many would he sell?

Answer 1

  $P = commodity Y's price.$  

  $Q is equal to the commodity Y's quantity$ .

Monopolist demand curve, $(Q) = 50 - 2.5P$

The Inverse demand curve,        $P = 20 - \frac{ 10Q }{25 }$

Monopolist has Quantity as $(Q) = 50$

Y's Production cost          $= 0$

$Total revenue = PQ$

$= (50-2.5P)P$

$=50P - 2.5P^2$

$Differentiate with respect to P,and equated to 0$

$= 50-2.5p$ $= 0$

$50= 2.5$ $P$

$P =\frac{ 50}{2.5}$

$P= 20$

For the case of 100 units,

$100 = 50-2.5P$

$100-50 = 2.5p$

$P= \frac{50}{2.5}$

$P = 20 units$