1. A monopolist faces a demand curve of P = 22 - Q/(100z) and costs of c = 2 + z^2, where z is product quality. 2. Higher quality (higher z) increases demand by making Q more sensitive to changes in P. 3. If the firm must choose z = 1, 2, or 3, z = 1 will maximize profits because it has the highest profit per unit of $18.99 compared to $15.995 and $10.997 for z = 2 and z = 3, respectively.

1. 1. A monopolist faces the inverse demand curve P = 22 ? Q/(100z), where z is an index of
quality. The monopolist incurs a cost per unit of c = 2 + z^(2) .
(a) How do increases in product quality z affect demand?
(b) Imagine the firm must choose one of three quality levels z = 1, z = 2 and z = 3. Which quality
choice will maximize the firm
Solution
A. P = 22 - Q/(100z)
Q = 100z x (22 - P)
Thus, from the normal equation of demand curve we can see that there is a direct relation
between Z and Q which means Increase in Z will increase the Q. Thus, we can conclude that
increase in the product quality Z will also result in increase in the demand of the product.
B. 1. Z = 1
Profit per Unit = Price - Cost
Price = 22 - 1/(100 x 1) = $21.99
Cost = 2 + 1^2 = $3
Profit per unit = 21.99 - 3 = $18.99
2. Z = 2
Profit per Unit = Price - Cost
Price = 22 - 1/(100 x 2) = $21.995
Cost = 2 + 2^2 = $6
Profit per unit = 21.99 - 3 = $15.995
3. Z = 3
Profit per Unit = Price - Cost
Price = 22 - 1/(100 x 3) = $21.997
Cost = 2 + 3^2 = $11
Profit per unit = 21.997 - 11 = $10.997
Thus, at Z =1 the the firm will maximize its profit.