Question

DT is in lock-down and can only spend his time watching Fox News F or sending twitter messages T. His other option is to take time off and enjoy leisure G, that is, golfing. G is fixed at 8, leaving 16 hours for work. DT’s utility function is U(F,T,G)=10F(1/5) T(1/5) G(3/5). The utility generation from time spent watching Fox News, LF, and time spent sending twitter messages, LT, is driven by the following production functions F=LF(1/2)and T=LT(1/2). Note that the time spent working must add up to 16. How much time will an optimizing DT spend watching Fox News LF relative to twittering LT? Select one:

a. L subscript F greater than L subscript T

b. L subscript F less than L subscript T

c. L subscript F equals L subscript T

d. He is indifferent between any feasible allocation of time between the two activities.

Answer 1

We know that:

F + T = 16

Also it is given that:

F = Hence: L_F = F²

T = Hence: L_T = T²

Now, we know that DT wants to maximise his total utility L = L_F + L_T subject to his constraint of F + T = 16

Hence we can use the Marshallian Lagrangian method to maximise utility subject to a constraint.

M = L + U(16-F-T)

M = F² + T² + U(16-F-T)

Differentiating M wrt F,T,U and equating it to zero, we get:

dM/dU = M_U = 16 - F - T = 0

dM/dF = M_F = 2F - U = 0 Hence F = U/2

dM/dF = M_T = 2T - U = 0 Hence T = U/2

This indicates that F=T

Hence 16 = F + T = 2F

Hence F = T = 8.

Hence L_F = 8² = 64; L_T = 8² = 64.

Hence L_F = L_T

Hence answer is: Option c) L_F = L_T