Please solve this question:

Question:

1. A firm faces a demand function Q=180-110P (where Q = quantity demanded, and P = price), and a total cost function TC=5Q2+600Q+400 (where Q = output)

1. Calculate the point price elasticity of demand at P = 1000.

(4 marks)

2. Would a reduction in price from 1000 increase total revenue?

(2 marks)

1. Manipulate the demand function to obtain an expression for P in terms of Q.

(2 marks)

2. Using the definition for total revenue, TR = PQ, obtain an expression for TR; in terms of Q only.

(2 marks)

3. Obtain an expression for marginal revenue (MR) in terms of Q.

(2 marks)

4. Using the total cost (TC) function you have been given, obtain an expression for marginal cost (MC).

(2 marks)

5. Using the definition for profit, =TR-TC, write down an expression for in terms of Q only.

(2 marks)

6. Using optimisation find the profit maximising level of output.

(3 marks)

7. Show that your answer in (e) is a maximum point.

(2 marks)

8. What is the firms total profit at its profit maximising level of output?

(2 marks)

1. If the firm produces at the profit maximising level of output, what is the price?

(2 marks)

Please solve all question;