The Democratic People's Republic of Gruberland has two workers in its economy: worker A and worker B. Workers choose a combination of leisure and consumption to maximize their utility. The individual utility functions are as follows:

UA=C^(7/8) * Z^(1/8)

UB=C^(1/2)+(30Z)^(1/2)

whereCstands for consumption, andZstands for leisure. Any given worker is constrained by a maximum of24hours of leisure, or a maximum of24hours spent working for an hourly wage,w. One unit of consumption costs $1.

Find the expression for the individual labor supply functions,LA(w)andLB(w)for each worker. To demonstrate that you have found the correct labor supply functions, solve for the labor supplies ifw=10.