An airline is deciding how to structure this year’s passenger booking process. The airline uses both sales agents and an online scheduling platform that must be continuously monitored, updated and debugged. Currently, the airline pays computer programmers $20 per hour and sales agents $10 per hour. The bookings per hour is represented by the following Cobb-Douglas function: f(x)=x1^2/3 x2^1/3

where f is the bookings per day, x1 is the number of computer programmer hours per day and x2 is the number of sales agent hours per day.

Required:
a. Show that the elasticity of the quantity produced with respect to computer programmer hours is 2/3 Show that the elasticity with respect to sales agent hours is 1/3
b. Find the marginal product of computer programmer hours and sales agent hours.
c. The airline would like on average 1,000 bookings per day. Find the number of computer programmer hours per day (x1) and the number of sales agent hours per day (x2)
d. A sudden increase in the need for computer programmers by companies in other industries has significantly increased the wages of computer programmers. How do the number of hours per day for computer programmers and sales agents change when computer programmers are instead paid $160 per hour (W1 = $160, W2= $10)?
e. Have the sales agents benefited from the increase in programmers' hourly wage? Have the computer programmers benefited?