1) A firm faces a demand function = 100 1 2 (where =quantity demanded, and =price), and a total cost function = 2 2 + 120 (where =output):

a) Manipulate the demand function to obtain an expression for in terms of (1 mark)

b) Using the definition for total revenue, = , obtain an expression for in terms of only (1 mark)

c) Obtain an expressions for marginal revenue () in terms of (1 mark)

d) Using the total cost () function you have been given, obtain an expression for marginal cost () (2 marks)

e) Using the definition for profit, = , write down an expression for in terms of only (2 marks)

f) i) Using optimisation, find the profit maximising level of output (4 marks) ii) Show that this is a maximum point (2 marks) ii) Show that MR=MC at this level of output (2 marks)

g) Using the expressions you have derived: i) Calculate the level of output at which total revenue () is maximised. (3 marks) ii) Calculate the level of output at which the firm will just break even. (3 marks)