The Excel file "Assignment Data" depicts data on monthly quantities of output (Q), capital (K), and labor (L). Using these data and the regression analysis, please do the following:

(a) Estimate the linear production function. Find the optimized profit if w = $25, r = $10, P = $10, and production target of 100 units of output.

Conducting the regression analysis, we can get the expression of linear production function as follows:

Q=114.34+2.34L+0.47K

(b) Estimate the Cobb-Douglas production function without the productivity parameter (suppress the intercept term).

(c) Estimate the Cobb-Douglas production function with the productivity parameter.

(d) Using your answer from (c), please answer:

(i) Does this production function feature increasing, decreasing, or constant returns to scale?

(ii) find the optimal mix of inputs for a budget of $10,000 if w = $25 and r = $50.

(iii) What is the profit if P = $100?

?Note: Due to uploading the Excel File to the platform is prohibited, I paste the Excel data as follows?

Q 657.29 935.93 1110.65 1200.89 1052.68 3406.02 2427.89 4257.46 1625.19 1272.05 1004.45 598.87 853.1 1165.63 1917.55 9849.17 1088.27 8095.63 3175.39 1653.38 5159.31 3378.4 592.85 1601.98 2065.85 2293.87 745.67

L 162.31 214.43 186.44 245.83 211.4 690.61 452.79 714.2 320.54 253.17 236.44 140.73 145.04 240.27 536.73 1564.83 214.62 1083.1 521.74 304.85 835.69 284 150.77 259.91 497.6 275.2 137

K 279.99 542.5 721.51 1167.68 811.77 4558.02 3069.91 5585.01 1618.75 1562.08 662.04 875.37 1696.98 1078.79 2109.34 13989.55 884.24 9119.7 5686.99 1701.06 5206.36 3288.72 357.32 2031.93 2492.98 1711.74 768.59