Question

3.The monopolist faces a demand curve given by D(p) = 10p-3 . Its cost function is c(y) = 2y. What is its optimal level of output and price?.

Answer 1

To find the monopolist's optimal level of output and price, we set marginal revenue equal to marginal cost. The optimal level of output is 47 units and the optimal price is $5.

Step-by-step explanation:

In order to determine the monopolist's optimal level of output and price, we need to find the point where marginal revenue (MR) equals marginal cost (MC). The monopolist's demand curve is given by D(p) = 10p-3, and the cost function is c(y) = 2y.

First, we calculate the monopolist's marginal revenue (MR) by finding the derivative of the demand curve with respect to quantity:

MR = 10 - 3/10p

Next, we set MR equal to MC to find the profit-maximizing level of output:

10 - 3/10p = 2

Simplifying the equation, we get:

10p - 30 = 20

10p = 50

p = 5

Finally, we substitute the optimal price back into the demand curve to find the optimal level of output:

D(p) = 10(5) - 3

D(p) = 50 - 3

D(p) = 47

Therefore, the monopolist's optimal level of output is 47 units and the optimal price is $5.

Answer 2

-> R (y) = (10y -3) 2y = 20y² - 6y -> R' (y) = 40y - 6 Optimal level of output when R' (y) = C'(y) -> 40y - 6 = 2 => 40y = 8 => y = 8/40 = .2 by using differential calculus w got its optimal level and price