See the data below. As the General Manager of hotel resorts, you seek to understand the relationship between the number of vacation packages provided and hours of labour expended in providing this service. From resort hotels’ records (accounting, human resources, and marketing departments), you collected four years of monthly data on the following variables: the number of vacation packages provided (Q) and the hours of labour expended in providing the service (L). Additionally, you know that the hourly wage is $15, and the price of a vacation package is $700. You want to calculate the profit-maximizing number of labour hours.

a. Estimate the following production function: Q = αLβ, where α and β are the coefficients. First, log-linearise the production function and then estimate the log-linear regression equation. Copy and paste your regression results from your excel file, and write down your estimated function in this form: Q = αLβ.

b.Using the function in (a), derive the marginal product of labour (MPL) and plot it against L in Excel. Copy and paste your plot into your assignment.

c. Does this production function exhibit diminishing marginal returns to labour? Explain. Hint: How does MPL depend on L?

d. You are currently employing L = 5,215. Is this number optimal? To answer this question, compare the value of the marginal product at L = 5,215 with the hourly wage. Should the number of labour hours employed be increased, decreased, or kept unchanged in order to maximize profits?

e. Find the profit-maximizing number of labour hours mathematically.

Q	L
338	5215
361	6623
382	6859
406	7948
308	4560
324	5081
311	5383
311	4410
301	4294
296	3913
321	6116
550	25411
461	18043
283	3351
377	7038
360	5719
314	4248
314	5036
310	4278
334	5175
306	4343
305	4675
293	3985
527	16359
559	27389
319	5875
375	7021
342	7123
408	10989
357	6626
317	4389
330	5530
288	3586
315	4721
291	4685
487	19869
533	22663
320	4700
297	3723
333	6745
359	7876
329	5181
308	4838
323	6014
276	3424
308	4634
293	3523
428	12484