Production Function Estimation (16 points) Sophie's Fashion Boutique (SFB) is a private firm producing dresses. It mainly uses sewing machines and hires labor for the production. Sophie pays $15 per labor hour. And the cost of using a sewing machine per month (which includes depreciation and interest payments) is $20. (Please see the excel file in the portal).

a) Use the data to estimate the "production function" for SFB (i.e. the relationship between the quantity of dresses, the number of sewing machines, and the working hours used). Assume the production can be best described by a Cobb-Douglas production function. Include the regression results from Excel in your assignment.(Hint: for all estimated coefficients carry 4 non-zero digits to the right of the decimal).

b) Use your estimated producing function from part a) to find the optimal combination of sewing machines and working hours that produces 2, 000 dresses per month.

Data:

a) Use the data to estimate the "production function" for SFB (i.e. the relationship between the quantity of dresses, the number of sewing machines, and the working hours used). Assume the production can be best described by a Cobb-Douglas production function. Include the regression results from Excel in your assignment.(Hint: for all estimated coefficients carry 4 non-zero digits to the right of the decimal). b) Use your estimated producing function from part a) to find the optimal combination of sewing machines and working hours that produces 2, 000 dresses per month. I' ------------------------------------------------------- I I _ I A B C Q K F 500 3 534 50 2 96 340 3 324 900 4 589 1350 4 813 240 3 268 40 2 69 1050 4 743 520 3 604 70 2 128 240 3 278 75 2 165 90 2 194 280 3 297 960 4 637 95 2 176 570 4 397 525 4 389 1480 5 727 2450 6 978 3150 6 1287 2300 6 912 660 4 417 360 3 369 65 2 118 900 4 578 1880 5 961 4500 1503 2750 6 1143 160 3 154