John is the owner of a factory producing solar panels in Nooneknow. John sells his products in the local market, and he would like to maximize the profit of his business. Below are the demand, the relevant marginal revenue and the marginal cost of John’s product.
Quantity demanded per day: Q = 10 – P, where P is the price of solar panel;
Marginal revenue per day: MR = 10 – 2Q;
Marginal cost: MC = 6;
For example, when P = 9, the quantity demanded per day Q is 1, and MR is 8.
(i) How many solar panels should John’s factory produce every day? What is the profit-maximization price? Explain your answer briefly.
(ii) Suppose that John’s business is earning a profit of 3 per day at the optimal output, i.e. your answer to (i). What is the total fixed cost of John’s business?
(iii) Now the government of Nooneknow imposes a unit tax of 2 per solar panel sold. Briefly explain how this unit tax might affect John's factory's optimal price and output.