Precision Engineering department has collected data on its average costs of production for the past 12 months. The monthly fixed cost is $4000 per month. The AVC and associated output data are presented below:

(a) Precision Engineering is a perfectly competitive firm. Based on the information above, explain if AVC suggests the functional form: AVC = a + bQ + cQ2. (Draw a scatter diagram of AVC on Y axis and Q on X axis. Fit the scatter diagram with a 2nd degree polynomial trend line.)  

(b) Run the appropriate regression to calculate the estimated parameters for the empirical cost function AVC = a + bQ + cQ2. Your answer should include regression output from the statistical software.  

(c) Show the level of output at which AVC reach its minimum value, and the minimum value of AVC at its minimum.

(d) Explain the significant point in determining the shut down condition of Precision Engineering department.

(e) Show what is the optimal level of monthly production for Precision Engineering department if the market price of each component is $400 per piece? What is the maximum profit or minimum loss Precision Engineering department can expect to earn? 

Additional Information

This kinds of problem is a part of  Statistics and it is about calculating the functional form of AVC or average variable cost for Precision Engineering department. The data from the department has been used for statistical calculations such as calculation of functional form, estimated parameters for empirical cost function, optimal level of monthly production, etc. have been answered in the solution in detail.