Question: The quantity produced (in thousands) and the average cost (in dollars) of producing a toy at different plants are shown here.

Plant Average Cost Quantity (Quantity)^2

1 $0.75 100 10,000

2 0.40 200 40,000

3 0.50 140 19,600

4 0.60 260 67,600

5 0.45 160 25,600

6 0.55 120 14,400

7 0.70 280 78,400

8 0.45 180 32,400

9 0.40 220 48,400

10 0.45 240 57,600

a. Use regression analysis to estimate average cost as a linear function of quantity produced. Write the equation, t-statistics, and coefficient of determination. Does the equation exhibit increasing, decreasing, or constant returns to scale?

b. Use regression analysis to estimate average cost as a linear function of quantity and quantity squared (e.g., the quantity and quantity squared data for plant 1 would be 100 and 10,000, respectively). Determine the equation, t-statistics, and coefficient of determination. At what quantity is average cost a minimum? Over what range of output are increasing returns to scale indicated? What about decreasing returns to scale?

c. Using the results from part (b), what is the minimum output necessary to break even at a price of $0.55?