The following is a table of the total cost (TC) of producing output Q for a particular firm. Based on this information, which of the following statements is correct? Select one cor... The following is a table of the total cost (TC) of producing output Q for a particular firm. Based on this information, which of the following statements is correct? Select one correct answer: a. The average cost at Q = 40 is £3. b. The marginal cost at Q = 60 is £6.50. c. The marginal cost is higher than the average cost at Q = 20. d. The marginal cost curve intersects the average cost curve at Q = 60. Read more

Steps to Solve

1. Calculate Average Cost (AC) at Q = 40
   To find the average cost, use the formula:
   $$ AC = \frac{TC}{Q} $$
   For Q = 40, TC = 180:
   $$ AC = \frac{180}{40} = 4.5 $$
   So, AC at Q = 40 is £4.5, not £3.

2. Calculate Marginal Cost (MC) at Q = 60
   To find the marginal cost, use the formula:
   $$ MC = TC(Q) - TC(Q - 1) $$
   For Q = 60 and Q = 40:
   $$ MC = 270 - 180 = 90 $$
   The marginal cost at Q = 60 is £90, not £6.50.

3. Compare Marginal Cost and Average Cost at Q = 20
   For Q = 20, TC = 120:
   $$ AC = \frac{120}{20} = 6 $$
   Calculate MC between Q = 20 and Q = 40:
   $$ MC = 180 - 120 = 60 $$
   Since MC (£60) is higher than AC (£6), this statement is true.

4. Determine the intersection of MC and AC
   The marginal cost intersects average cost where MC = AC. We have:

• For Q = 40: AC = £4.5, MC calculation is needed for ranges (not yet calculated for other points). However, we already see that AC is decreasing and MC significantly higher at least until Q=60.

Since we saw MC > AC at Q = 20, it suggests that they will likely intersect at a higher Q value.