Question
Suppose a competitive firm has a total cost function TC(q)=450+15q+2?2 and marginal cost
function MC(q)=15+4q. If the market price is P=Rs 115 per unit,
(i) Find the level of output produced by the firm.
(ii) Find the level of profit and the level of producer surplus.
Answer :
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For a competitive firm, the profit-maximising condition is that the firm produces the level of output where price is equal to marginal cost, provided the price covers the average variable cost. The given functions are: [ TC(q)=450+15q+2q^2 ] and [ MC(q)=15+4q ] The market price is: [ P=Rs,115 ] Since the firm is perfectly competitive, price is equal to marginal revenue: [ P=MR=Rs,115 ] The firm maximises profit by producing where: [ MR=MC ] Therefore, [ 115=15+4q ] [ 4q=100 ] [ q=25 ] Thus, the profit-maximising level of output is: [ \boxed{q=25\text{ units}} ] To verify the shutdown condition, calculate average variable cost. Total cost is: [ TC=450+15q+2q^2 ] The fixed cost is Rs 450, while variable cost is: [ VC=15q+2q^2 ] Hence, [ AVC=\frac{VC}{q}=15+2q ] At (q=25), [ AVC=15+2(25)=65 ] Since the market price is Rs 115 and: [ P>AVC ] the firm will continue production. Therefore, (q=25) is the appropriate short-run profit-maximising output. For the second part, the firm's total revenue is: [ TR=P\times q ] Substituting the values: [ TR=115\times25 ] [ TR=2875 ] Thus, total revenue is Rs 2,875. Now calculate total
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