Suppose that the total monthly cost of manufacturing is TC = 15,000 – 50Q + 0.5Q2

Question

Suppose that the total monthly cost of manufacturing is TC = 15,000 – 50Q + 0.5Q2  

 

1. Determine the total marginal cost equation and the average cost equation. 
2. Determine the level of production that results in the smallest average production cost. 
3. Determine the level of Q for which the average cost is equal to marginal cost. 
4. What can you deduce from your results obtained in problems 2 and 3? 

Answer 1

1. To find MC, differentiate the TC equation. MC = -50 + Q. To find AC, divide TC by Q. AC = (15,000/Q) - 50 + 0.5Q
2. Here you need to minimize the AC function. Take the First order condition (FOC). FOC = (-15,000/Q^2) + 0.5, set it equal to 0, and solve for Q. You'll get Q = 173.2. You can check whether it is a minimum by confirming the second order condition is positive.
3. Set MC = AC, and solve for Q. Q = 173.2
4. You can deduce that the MC curve intersects the AC curve at its minimum.