In: Economics

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.

i).

TR = P.Q

Q = 130-10P

10P = 130-Q

P = 13-Q/10

TR = (13-Q/10)*Q = 13Q-0.1Q^{2}

TC = FC+VC

TC = 60+4Q

ii).

Firm breaks even where TR = TC

13Q-0.1Q^{2}=60+4Q

-0.1Q^{2}+9Q-60=0

Using quadratic formula

a=-0.1, b=9, c=-60

iii).

iv).

Profit = TR-TC

Profit = 13Q-0.1Q^{2}-60-4Q=-0.1Q^{2}+9Q-60

Firms break even where total revenue (TR) is equal to total cost (TC).

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