Question

20. value: 7.00 points Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = 2BW where B is the amount of bananas she consumes and W the amount of water. Her production function for bananas is B = 2Lp where Lp 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 20, what should she do to maximize her utility? (Enter your answer in whole numbers.) LB Lw=

Answer 1

Given U=2BW

B=2L_B or L_B=B/2

W=2L_W or L_W=W/2

Also L_B+L_W=20

So,

(B/2)+(W/2)=20

B+W=40

or 40-B-W=0

Now maximize U=2BW subject to 40-B-W=0

i.e.

L = 2BW - X(40 - B-W)

First order conditions give us

dL/dB = 2W -X=0

or ------(1)

= 21

dL/DW = 2B-X=0

------(2)

= 2B

From equation (1) and equation (2), we get

2W=2B

W=B

We know that B+W=40

Set W=B

B+B=40

B*=20

W*=B*=20

L_B*=B/2=10

Lw*=W/2=10