Question: Suppose that the inverse demand function is given by \(p=100-q\) and the cost function is given by \(T C=q^{2}+4 q+10\)

1. What is the optimum amount of output and the market price 1n a monopolistic
   market? (Hint: a monopolist can influence the price) .
2. What is the amount of output and the market price if the monopolist behave as a
   price taker — i.e., set the price similar to a firm in a perfectly competitive market?
3. Use two well labelled graphs to show the amount of output, the market price and/or profits under each market condition. In one graph depict the total revenue and total cost. In another graph depict the demand, marginal revenue and supply curves.
   Bonus:
4. What is the optimum amount of output and the market price in a perfectly competitive market if there are 10 firms in the market in the short-run? (Hint: in the short—run the number of firms in the market is fixed and a competitive firm cannot influence the price)
5. What is the optimum amount of output in a perfectly competitive market in the

long-run?

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