The fixed estimated cost of new production is $250,000 and the average variable cost is:

AVC = $10 + $0.01Q

where Q = Output

(a)

The total cost (TC) and average total cost (ATC) at quantity 4,000 can be calculated as:

TC = FC + VCTC = $250,000 + $10Q + $0.01Q2TC = $250,000 + $10 × 4,000 + 0.01 × 4,0002TC = $450,000TC = FC + VCTC = $250,000 + $10Q + $0.01Q2TC = $250,000 + $10 × 4,000 + 0.01 × 4,0002TC = $450,000

Average total cost at 4,000 quantities is:

ATC =TCQATC =$450,0004,000ATC = $112.5ATC =TCQATC =$450,0004,000ATC = $112.5

(b)

With greater productivity, the total cost was $522,500 at volume of 5,000 cases. The effect of learning on average total cost (AC) can be calculated as:

Learning effect = Actual AC - Estimated AC

The estimated average cost at 5,000 cases is:

AC =TCQAC =$522,5005,000AC = $104.5AC =TCQAC =$522,5005,000AC = $104.5

The estimated average cost at 5,000 cases is:

TC = $250,000 + $10 × 5,000 + 0.01 × 5,0002TC = $550,000AC =550,0005,000AC = $110TC = $250,000 + $10 × 5,000 + 0.01 × 5,0002TC = $550,000AC =550,0005,000AC = $110

Learning effect = $104.5 - $110

Learning effect = - $5.5 per case