Question

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

If the total time she has available is 10, what should she do to maximize her utility? (Enter your answers in whole numbers.)
LB =
LW =

Answer 1

To maximize her utility, Elsa should allocate all her available labor time to bananas (LB = 10) and water (LW = 0).

To maximize her utility, Elsa should allocate her labor time between bananas and water in a way that maximizes her utility function U = BW. Since her production function for bananas is B = 2LB and her production function for water is W = 2LW, she needs to find the values of LB and LW that will maximize her utility.

Given that Elsa has a total of 10 hours available and her utility function is U = BW, she needs to find the values of LB and LW that maximize U = B*W = (2LB)(2LW) = 4LB*LW.

We can solve this problem using calculus by taking the partial derivative of U with respect to LB and LW and setting them equal to zero. This will give us the values of LB and LW that maximize U.

Taking the partial derivative of U with respect to LB, we get dU/dLB = 4LW = 0. Solving for LW, we find that LW = 0.

Taking the partial derivative of U with respect to LW, we get dU/dLW = 4LB = 0. Solving for LB, we find that LB = 0.

Therefore, to maximize her utility, Elsa should allocate all her available labor time to bananas (LB = 10) and water (LW = 0).