P = $130 - $0.000125Q
MR - $130 - 0.00025
Fixed development cost = $600,000
Marginal costs are $63 per unit.
Calculate output, price, total revenue and total profit at the revenue maximizing activity level and then at the profit maximizing level (present each with relevant diagrams).
At the profit maximizing activity level,
II = TR - TC,
Here, II = 130Q - 0.000125Q^2 - 600,000 - 63Q
= 67Q - 0.000125Q^2 - 600,000
Now, setting the profit-maximizing level, from which any extra profit is not possible,
dII / dQ = 67 - 0.00025Q* = 0
II Q* = 67 / 0.00025 = 268,000
where, II = Profit, TR = Total Revenue, TC ...
The solutions uses the data given in the question and calculates output, price, total revenue and total profits. Relevant diagrams are also presented in the response. Step by step calculations have been provided which makes it really easy to follow along. A student downloading this solution can easily understand the concepts and then apply them to similar problems. Overall, an excellent response that provides clear and detailed explanation to the problem being asked.