The firm produces goods in perfect competition and sells them at a price of 600 rubles. The total cost function has

| December 25, 2020 | education

The firm produces goods in perfect competition and sells them at a price of 600 rubles. The total cost function has an id: ТС = 154 + 24Q + 3Q3. Determine: a) the optimal volume of the firm’s output; b) the size of its profit; c) the price at which the company would operate without profit, but also without losses.

a) The condition for maximizing profit for a competitive firm is expressed by the formula: MC = MR = P We know that MC = TC` (Q) MC = 24 + 9Q2 24 + 9Q2 = 600 9Q2 = 576 Q2 = 64 Q = 8 – optimal output products
b) Next, we find the profit of the company, for this we need to find the difference between the total revenue (TR) and total costs (TC) Pr = TR – ТС We find the unknown TR according to the formula TR = P * Q TR = 600 * 8 = 4800 tr. We find TC by the formula from the condition TC = 154 + 24Q + 3Q3 = 154 + 24 * 8 + 3 * 8 ^ 3 = 154 + 192 + 1536 = 1882 tr. Hence Pr = 4800-1882 = 2918 tr.
c) The firm operates without profit or loss in the case when the total revenue and total costs are equal. Pr = 0 => TR = TC P * Q = 154 + 24Q + 3Q3 P = (154 + 24Q + 3Q3) / Q Substitute Q = 8 and get P = (154 + 24 * 8 + 3 * 8 ^ 3) / 8 = (154 + 192 + 1536) /8=1882/8=235.25 tr.
Answer: a) Q = 8 b) Pr = 2918 tr. c) P = 235.25 tr.



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