Short-run demand and total cost functions for a monopoly firm are as under: Demand function : Q = 100 – 0.2 P Price function : P = 500 – 5 Q Cost function : TC = 50 + 20 Q + Q2 Where Q = Total quantity of the product in physical units. P = Price of the product per unit TC = Total cost What is the profit maximizing output of the pure monopoly firm?

The profit maximizing output of a pure monopoly firm is the output level at which marginal revenue equals marginal cost. In this case, the demand function is $Q = 100 – 0.2P$, the price function is $P = 500 – 5Q$, and the cost function is $TC = 50 + 20Q + Q^2$.

To find the profit maximizing output, we first need to find the marginal revenue and marginal cost functions. The marginal revenue function is found by taking the derivative of the demand function with respect to quantity, which gives us $MR = -0.4Q + 100$. The marginal cost function is found by taking the derivative of the cost function with respect to quantity, which gives us $MC = 20 + 2Q$.

We can find the profit maximizing output by setting marginal revenue equal to marginal cost and solving for $Q$. This gives us the equation $-0.4Q + 100 = 20 + 2Q$. Solving for $Q$, we get $Q = 35$.

Therefore, the profit maximizing output of the pure monopoly firm is 35 units.

Here is a brief explanation of each option:

• Option A: 20 units. This is not the profit maximizing output because marginal revenue is greater than marginal cost at this output level.
• Option B: 35 units. This is the profit maximizing output because marginal revenue equals marginal cost at this output level.
• Option C: 40 units. This is not the profit maximizing output because marginal cost is greater than marginal revenue at this output level.
• Option D: 50 units. This is not the profit maximizing output because marginal revenue is less than marginal cost at this output level.