ABC Machinery produces ice machine with historical (monthly) data in the Excel file. Please construct its short-run total cost function to answer the following questions:

Question

QUESTIONS
1. Given the data, please construct a Short-Run total cost (TC) function (cubic function) by Excel regression for ABC Machinery. (20%)

2. Given your answer in 1, please indicate how much the fixed cost (FC) is and what the marginal cost (MC) function is. (20%)

3. Please comment on whether the estimated function in question 1 is a good fit or not. What is the interpretation of coefficient of determination (R-square)? Does the regression show overall significance at 5%? (20%)

4. How much will be the total costs if ABC Machinery produces 200 ice machines in a month? Please show your calculation. (20%)

5. Assume that the marginal revenue (MR) function (at unit of $1,000) of ABC ice machine is
MR = 30 − 0.1Q

In order to maximize the monthly profit, what will be the optimal output level? Please show your calculation. (20%)

(Hint: Make MR=MC then apply the quadratic formula to solve the equation.)

Data
ABC Machinery
Total Cost ($1,000) Output Rate (Q)
2251 121
1866 62
2310 153
2407 187
2109 87
2523 204
1726 43
2201 110
2170 92
1812 54
2736 233
2290 141
1910 66
2894 271
2277 139