Question

TC = 125000 + 7000Q - 35Q2 + 0.03Q3
         where TC = total costs in dollars and Q = number of outputs in units.

          Which statement is correct?

         (a) ATC = (125000 / Q) + 7000 - 70Q + 0.03Q2
              (b) If diminishing returns occur at the minimum MC, then the company
                    will experience diminishing returns for Q> 583.3
(c) The function above is a short-term cost function
              (d) All of the answers above are correct

Answer 1

The correct answer is  (d) All of the answers above are correct

ATC = TC/Q => ATC = (125000 + 7000Q - 35Q² + 0.03Q³)/Q

=> ATC =  125000/Q + 7000 - 35Q + 0.03Q²

Hence Option (a) is correct

When Diminishing Marginal returns sets in Marginal Productivity(MP) is diminishing and as cost is opposite to production => MC is increasing. Initially there is increasing returns and then there is diminishing returns and Hence, MC is initially decreasing and then after it reaches its minimum and when diminishing returns sets in it starts increasing => MC is increasing when diminishing returns sets in.

for diminishing returns range of Q, We have to find range of Q at which MC is increasing

MC = dTC/dQ = 7000 - 2*35Q + 3*0.03Q² = 7000- 70Q + 0.09Q²

dMC/dQ = -70 + 0.18Q > 0 => Q > 70/0.18 => Q > 388.89

Hence, for Q > 583.3, there is diminishing returns

Hence option (b) is correct.

A function is a short run if it incur cost even if they are not producing anything i.e. TC > 0 when Q = 0

TC = 125000 + 7000Q - 35Q² + 0.03Q³

=> When Q = 0, TC = 125000 + 7000*0 - 35*0 + 0.03*0 = 125000

Hence There is cost of 125000 even if production (Q) = 0. This cost is called fixed cost.

Hence, this is a short run cost function.

Note there is no Fixed cost in the long run.

Hence this option (c) is also correct.

Hence all of them are correct.

Hence, the correct answer is  (d) All of the answers above are correct