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. Given the following data for a perfectly competitive firm, what is the amount of profit the firm will make atthe profit maximizing output? AR = $100 and TC = 1,000 + 125Q - .5Q2 where Q = units produced permonthA) none – the firm would shut downB) $1,312.50C) $2,548.63D) –$1,425.86E) –$2,351.27

Question

. Given the following data for a perfectly competitive firm, what is the amount of profit the firm will make atthe profit maximizing output? AR = 100andTC=1,000+125Q−.5Q2whereQ=unitsproducedpermonthA)none–thefirmwouldshutdownB)100 and TC = 1,000 + 125Q - .5Q2 where Q = units produced permonthA) none – the firm would shut downB) 1,312.50C) 2,548.63D)–2,548.63D) –1,425.86E) –$2,351.27

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Solution

To find the profit maximizing output, we first need to find the quantity (Q) where marginal cost (MC) equals marginal revenue (MR).

  1. First, we need to find the MC. The total cost (TC) function is given as TC = 1,000 + 125Q - 0.5Q^2. The marginal cost (MC) is the derivative of the total cost function with respect to Q.

    MC = d(TC)/dQ = 125 - Q

  2. In a perfectly competitive market, the average revenue (AR) equals the marginal revenue (MR). So, MR = AR = $100.

  3. Set MC equal to MR to find the profit maximizing quantity:

    125 - Q = 100 Q = 25

  4. Substitute Q = 25 into the total cost function to find the total cost at this quantity:

    TC = 1,000 + 125(25) - 0.5(25)^2 TC = 1,000 + 3,125 - 312.5 TC = $3,812.50

  5. The total revenue (TR) is price times quantity, or AR*Q = 100∗25=100*25 = 2,500.

  6. Finally, subtract the total cost from the total revenue to find the profit:

    Profit = TR - TC = 2,500−2,500 - 3,812.50 = -$1,312.50

So, the firm would make a loss of 1,312.50attheprofitmaximizingoutput.Therefore,theansweris(D)–1,312.50 at the profit maximizing output. Therefore, the answer is (D) –1,312.50.

This problem has been solved

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