Table one below consists of 12 prospective plant sizes that would produce between 30 and 60 cubic yards of concrete per hour. As you can see there are 4 different combinations of capital (K) and labor (L) for each of three different capacities. For ease of analysis the units of capital and labor have been standardized. Table two shows the results of a linear regression estimating hourly demand in the new city, for ease of analysis just assume a household income of $65,000.

It is projected that a unit of capital will increase costs( depreciation, repairs, maintenance, interest expense , utilities) to the firm by $18,000 a year based on a working year of 260 eight-hour working days. Presently, the firm can hire labor at an average of $7.00 an hour. However, the founder wants an analysis using $7.00 and also $8.50 as he may have to pay higher labor costs in the other city as its unemployment rate is lower.

Other costs for a cubic yard of concrete include:

Gravel $3.34

Cement $7.50

Average delivery costs $4.00

Do a report that include a comparison of the costs associated with all of the feasible plants and what sort of returns to scale this production function typifies. You should also analyze the estimated demand curve looking at the total and marginal revenue functions. Given the foregoing you should outline a profit maximizing production goal.

The owner has asked you to run a simulation in which plant 10 is built and $96,000 of the capital costs are fixed. He wants to know what level of output needs to be achieved to break even at cubic yard price of $19.00, $20.00, and $21.00.

Finally you should make a recommendation as to whether to build or not, and if to build what size.

Table One Plant 1 K=4 L=1 Plant 4 K= 1 L = 10 Plant 5 K= 6 L=1.5 Q=30 yards per hour Plant 2 Plant 3 K=3 K= 2 L = 2 L=5 Q= 45 yards per hour Plant 6 Plant 7 K=4.5 K=3 L=3 L = 7.5 Q=60 yards per hour Plant 10 Plant 11 K= 6 K=4 L=4 L = 10 Plant 8 K=1.5 L= 15 Plant 9 K=8 L=2 Plant 12 K= 2 L=20 Table Two SUMMARY OUTPUT Regression Statistics Multiple R 0.98 R Square 0.96 Adjusted R Square 0.94 Standard Error 5.33 Observations 7 ANOVA df F 47.20 Significance F 0.00 Regression Residual Total 2 4 SS MS 2686.18 1343.09 113.82 28.46 2800.00 6 Intercept Price Income Coefficients 239.07 -9.41 0.00104 Standard Error 93.89 2.75 0.000549 Stat 2.55 -3.43 0.19 P- value 0.06 0.03 Lower 95% Upper 95% -21.61 499.75 -17.04 -1.78 0.00 0.00 0.86 Table One Plant 1 K=4 L=1 Plant 4 K= 1 L = 10 Plant 5 K= 6 L=1.5 Q=30 yards per hour Plant 2 Plant 3 K=3 K= 2 L = 2 L=5 Q= 45 yards per hour Plant 6 Plant 7 K=4.5 K=3 L=3 L = 7.5 Q=60 yards per hour Plant 10 Plant 11 K= 6 K=4 L=4 L = 10 Plant 8 K=1.5 L= 15 Plant 9 K=8 L=2 Plant 12 K= 2 L=20 Table Two SUMMARY OUTPUT Regression Statistics Multiple R 0.98 R Square 0.96 Adjusted R Square 0.94 Standard Error 5.33 Observations 7 ANOVA df F 47.20 Significance F 0.00 Regression Residual Total 2 4 SS MS 2686.18 1343.09 113.82 28.46 2800.00 6 Intercept Price Income Coefficients 239.07 -9.41 0.00104 Standard Error 93.89 2.75 0.000549 Stat 2.55 -3.43 0.19 P- value 0.06 0.03 Lower 95% Upper 95% -21.61 499.75 -17.04 -1.78 0.00 0.00 0.86