following are the information used to solve this problem
x= (Lx)0.5
y= 0.25(Ly)0.5
As Lx + Ly = 16
=> x2 + 16y2 = 16
utility for both = (xy)0.5
=>U(x)= (x0.5)*(1- x2/16)0.25
at equilibrium
dU/dx = 0
=> 0.5(x)-0.5 * (1- x2/16)0.25 + (x0.5) * 0.25(1- x2/16)-0.75 * (-2x/16) = 0
=> using this, we get x = 4,21.5,-21.5, -4, 0 as critical points.
so, Utility has maximum value at x = 21.5 or 2.83
Value of y = (1-x2 /16)0.5 = 1/(2)0.5 = 0.71
Maximum value of their utilities = (xy)0.5 = 1.42
following are the information used to solve this problem Joy the abandoned restaurant can be found...
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