The demand function for a good is given as Q = 130-10P. Fixed costs associated with producing that good are €60 and each unit produced costs an extra €4.
i). Obtain an expression for total revenue and total costs in terms of Q
ii). For what values of Q does the firm break even
iii). Obtain an expression for profit in terms of Q and sketch its graph
iv). Use the graph to confirm your answer to (ii) and to estimate maximum profit and the level of output for which profit is maximised.
TR = P.Q
Q = 130-10P
10P = 130-Q
P = 13-Q/10
TR = (13-Q/10)*Q = 13Q-0.1Q2
TC = FC+VC
TC = 60+4Q
Firm breaks even where TR = TC
Using quadratic formula
a=-0.1, b=9, c=-60
Profit = TR-TC
Profit = 13Q-0.1Q2-60-4Q=-0.1Q2+9Q-60
Firms break even where total revenue (TR) is equal to total cost (TC).