Please can someone give some ideas, even if they don't know the final solution?

A firm receives a price of 120 for its output. Its total cost function is C=.02Q^3 +.4Q^2 - 5Q - 15.

a) Assuming the utility operates to maximize profits, what is this firm's profit maximizing output level?

I know we have to use the quadratic formula to solve for Q:

Q= [-b +/- (b2 - 4 a c).5]/2a

Where a,b,c are from a quadratic equation as follows: a Q2 + b Q + c

If we get two positive solutions, one of them will be a minimum, and one a maximum. We can find the maximum by looking at the sign of the second derivative, evaluated at the two solutions.

b) What are revenues at the optimal level of output?

c) what are costs at the optimal level of output?

d) What are profits at the optimal level?

e). Now suppose a tax of $15.00 is levied on the sale of the output (electricity), which we will assume lowers the price the utility receives to $105.00. (We will have more say subsequently about how a tax burden is distributed between the supply side and the demand side of the market). What is the utility's profit maximizing output level, and its level of revenue, cost, and profit level now?

Solution Summary

Revenues at the optimal level of output are assessed.

... It also calculates associated profit with optimal output level. Total Output (Q) Price (P) Revenue (TR) (TC) Total Total Total Cost 0 1900 0 1000 1 1700 1700 ...

...Optimal price level is $35. Suppose that Figure 7.4 shows a monopolist's demand curve, marginal revenue, and its costs. At the profit maximizing output level, ...

... Solution describes the steps to find optimal output level and associated profit. Output Q Price, P Total Revenue Total Cost Marginal Revenue Marginal Cost ...

Selecting the optimal output level. Marginal revenue product is defined as the change in total revenue that results from the employment of an additional unit of ...

... A monopolist will set its output level such that MR=MC to ... 50*17.5+5*17.5^2=$2806.25 Total Revenue=P*Q ... depicts the steps to estimate the optimal output and price ...

... Profits=Total Revenue-Total Cost=10200-10200=0. ... Solution describes the steps to calculate optimal output levels and associated profits at the given price levels...