Final answer:
To compute the average and marginal cost starting from Q=2 up to Q=15, use the cubic total cost function to calculate the total cost at each quantity level. Then, find the average cost by dividing the total cost by the quantity produced. Finally, calculate the marginal cost by subtracting the previous total cost from the current total cost. The absolute value of the difference between average cost and marginal cost is minimized at a certain quantity.
Step-by-step explanation:
To compute the average and marginal cost starting from Q=2 up to Q=15, we first need to calculate the total cost (TC) at each quantity level using the cubic total cost function: TC(Q)=5+0.32*Q-0.25*Q^2+0.38*Q^3. Then, we can use the formula for average cost (AC = TC/Q) to find the average cost at each quantity level. Finally, the marginal cost (MC) can be calculated as the change in total cost divided by the change in output (MC = ∆TC/∆Q).
Here are the step-by-step calculations:
- For Q=2: TC(2) = 5+0.32*2-0.25*2^2+0.38*2^3 = 13.48. AC(2) = 13.48/2 = 6.74.
- For Q=3: TC(3) = 5+0.32*3-0.25*3^2+0.38*3^3 = 24.23. AC(3) = 24.23/3 = 8.08.
- Continue this process for Q=4, Q=5, and so on until Q=15.
- For Q=15: TC(15) = 5+0.32*15-0.25*15^2+0.38*15^3 = 705.48. AC(15) = 705.48/15 = 47.03.
- Now, calculate the marginal cost at each quantity level by subtracting the previous total cost from the current total cost. For example, MC(3) = TC(3) - TC(2) = 24.23 - 13.48 = 10.75.
The absolute value of the difference between average cost and marginal cost is minimized when the quantity produced is ______ units.