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You have a vegetable budget of $40. Carrots (C) cost $1, lettuce (L) cost $4. You’re...

  1. You have a vegetable budget of $40. Carrots (C) cost $1, lettuce (L) cost $4. You’re utility function is ?(?, ?) = 4?^1/2?^1/2.

    a) How many of each vegetable will you by such that you maximize your utility given your budget and prices?   b) Draw 3 budget constraints, including when income is $40 c) Draw 3 indifference curves, including a curve that includes your optimal bundle.
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Answer #1

a. U(C,L)=4C^1/2 L^1/2

MUc/MUL= L/C

Pc/PL=1/4

When utility is maximized, MUc/MUL=Pc/PL

4L=C....put this in budget constraint

Budget constraint:

C+4L=40

2C=40

C*=20

L*=20/4=5

Optimal amount of carrots=20, Optimal amount of lettuce=5.

b. Budget constraint 1 is BL1 with income $20.

BL2 with income $40

BL3 with income $60.

c. IC1 with utility =20

IC2 with utility =40

IC 3 with utility =60

Optimal bundle is point E where IC2 and BL2 intersect.

3 Lettuce C1. IC2. 103 A -5 0 5 10 15 20 25 30 35 40 45 50 Carrots -1

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