Question

Anna spends her income on green goods (G) and brown goods (B). Initially, Anna's income is $30, the price of green goods is $2, and the price of brown goods is $1. The government introduces a new regulation that increases the price of brown goods to $5.  

Her utility function is as before: U(G,B) = G^2B

Her marginal utility for green goods is: MUg = 2GB

Her marginal utility for brown goods is: MUg = G^2

a)Draw a clearly labeled graph showing the effect of the policy. The graph should include the initial, final, and decomposition baskets, as well as the corresponding indifference curves and budget lines.

b) Anna's compensating variation equals = $__?__

c) Anna's equivalent variation equals = $__?__

Answer 1

Answer b) • U(G,B) = G^2.B

At original bundle G*=B*= 10

U= 1000

1000= G^2.B

B= 1000/G^2

1) Differentiation B with respect to G = -2000/G^3

since,it is negative the IC will be downward sloping

2) Double derivative of B with respect to G= 6000/G^4

since it is positive IC will be convex shaped

• So the IC will be downward sloping convex shaped

• Original budget line: 30= 2G+ B

​​​​​​X intercept ( keeping B=0) = 15

Y intercept ( keeping G=0) = 30

• Original budget line is AB with Equilibrium E and Indifference curve IC1. The optimal Bundle is (10,10)

• New budget line: 30= 2G+5P

X intercept= 15

Y intercept= 6

• New budget line is A'B . New indifference curve is IC2 and new Equilibrium is E1 with bundle (10,2)