Suppose the demand function of a firm is given by Q + P – 20 = 0 and its total costs by TC -48 -4Q = 0. Find Profit as a function of output Q.   

REVIEW QUESTIONS

Question 1

1. Suppose the demand function of a firm is given by Q + P – 20 = 0 and its total costs by TC -48 -4Q = 0.
   • Find Profit as a function of output Q.                                                             (6)
   • With the use of quadratic formula find the intercepts for profit. (6)
   • Find the value of output that maximises Profit and the maximum Profit. (8)

Question 2

1. Suppose the demand function of a firm is given by Q + P – 20 = 0 and its total costs by TC -48 -4Q = 0.
   • Show with a diagram that Profit function reaches its maximum before TR. (12)
   • Compare the break-even points with the x-intercepts of the Profit function. (8)

Question 3

1. If fixed costs are 4, variable costs per unit are 3, and the demand function is:
   • Find TC and TR as functions of output Q.             (4)
   • With the use of quadratic formula find the intercepts for TR.             (5)
   • Find the coordinates of the break-even point. (5)
   • Comment on the values of Q less and greater than the first break-even point. (6)

Question 4

2. Given Total Revenue (TR) and Total Cost (TC), : and .
   • The minister of public enterprises is due to appear in Parliament and comes to you as an economist to advise on when is Eskom likely to reach its first break-even point. (6)
   • For the benefit of the minister also show where the Total revenue will be maximised and what is the maximum Total revenue? Hint: Minister understands differentiation better than any method. (6)
   • Summarise your findings above in a clearly labelled diagram for Minister’s presentation in Parliament, use different shading methods to differentiate losses from profits.                                                                                     (8)

Question 5

1. If fixed costs are 4, variable costs per unit are 3, and the demand function is:
   • Find The profit (as a function of output (Q).                                                          (5)
   • Find and solve for q.                                                                                               (5)
   • Prove that is a profit maximising condition.                                              (6)
   • Find the maximum profit. (4)

Question 6

1. Given Total Revenue (TR) and Total Cost (TC), : and .
   • Find The profit (as a function of output (Q).                                                          (5)
   • Find and solve for q.                                                                                               (5)
   • Prove that is a profit maximising condition.                                              (6)
   • Find the maximum profit. (4)

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