Suppose that the monopolistically competitive firm demand function given by the equation.P=11,100 -300Q and the firms TC function is given by the equation TC = 400,000 +300Q + 30Q² +300Q³?

To find the profit-maximizing level of output for the monopolistically competitive firm, we need to determine the level of output where marginal revenue (MR) equals marginal cost (MC).

First, let's find the total revenue (TR) function. Total revenue is calculated by multiplying the price (P) by the quantity (Q):

TR = P * Q = (11,100 - 300Q) * Q = 11,100Q - 300Q²

Next, we can find the marginal revenue (MR) function by taking the derivative of the total revenue function with respect to quantity:

MR = d(TR)/dQ = 11,100 - 600Q

Now, let's find the total cost (TC) function:

TC = 400,000 + 300Q + 30Q² + 300Q³

To find the marginal cost (MC) function, we take the derivative of the total cost function with respect to quantity:

MC = d(TC)/dQ = 300 + 60Q + 900Q²

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

11,100 - 600Q = 300 + 60Q + 900Q²

Rearranging the equation:

900Q² + 660Q - 10,800 = 0

We can solve this quadratic equation to find the values of Q. Once we have the values of Q, we can substitute them back into the demand function to find the corresponding prices (P).

Note: The solution to the quadratic equation may result in multiple values of Q, indicating that the firm may have multiple profit-maximizing levels of output.