Question

Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = 3BW where B is the amount of bananas she consumes and W the amount of water. Her production function for bananas is B = 2L_B where L_B is the amount of labour time she devotes to bananas. Her production function for water is W = 2L_W where L_W is the amount of labour time she devotes to water.

If the total time she has available is 100, what should she do to maximize her utility? (Enter your answer in whole numbers.)

L_B =

L_W =

Answer 1

Answer U= 3Bw B = 2LR and W = 2Lw Also LB + LW = Total time = 100 - Maximize : U= 3(240) (2LW) = 12 LBW I Subject to : L + LW = 100 (1) Legrange is given by L = 122640 & 1(100-LB-LW) first Order Condition 2620 = 12 w ĉ h alis al 20 = 12 LB =h a Lw L 12 Lw=h=1226 I LW = LB putting ins in (1) we get I Lot Lw=100 => Lw=50 = LB = LW = 50 Thus, ___ LB = 504 Lw=50