Final answer:
The profit-maximizing price and quantity for a monopoly firm with a constant marginal cost of 10 can be determined using the marginal revenue and marginal cost equations. If the marginal cost doubles, the new profit-maximizing price and quantity can be found by setting the new marginal cost equal to the marginal revenue equation. The original and new outcomes are P = $30, Q = 20 and P' = $35, Q' = 15, respectively.
Step-by-step explanation:
To determine the profit-maximizing price and quantity for a monopoly firm with a constant marginal cost of 10, we need to find the point where marginal revenue (MR) equals marginal cost (MC). The marginal revenue curve for a linear demand function is twice as steep as the demand curve itself. So, the marginal revenue equation is MR = 50 - 2Q, where Q is the quantity. Setting MR equal to MC gives us 50 - 2Q = 10.
By solving this equation, we find Q = 20 and substitute it back into the demand curve to find the price, which is P = 50 - Q = 30.
If the marginal cost were to double, the new marginal cost equation would be MC' = 20. The profit-maximizing quantity can be found by setting MR equal to MC', which gives us 50 - 2Q = 20. Solving this equation, we get Q = 15. Substituting Q back into the demand curve, the new price would be P' = 50 - Q = 35.
Therefore, the profit-maximizing price and quantity with the original cost are P = $30 and Q = 20, whereas with the doubled cost, the new price and quantity are P' = $35 and Q' = 15.