Task: 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.
Question 1: 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.
Question 2: What are revenues at the optimal level of output?
Question 3: What are costs at the optimal level of output?
Question 4: What are profits at the optimal level?
Question 5: 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?