Question

PLEASE HELP!!

3. Consider a world with one and only one type of food, called good 1, and a second non-food good called good 2. In an effort to prevent malnourishment, the government subsidizes food consumption up to a lower bound xL > 0: this is a per unit subsidy that reduces the unit price of food by 50% up to this amount. In an effort to reduce health costs, the government taxes food consumption above an upper bound xH > rL: this is a per unit tax that increases the unit price of additional food over and above this amount by 50%. Graph the budget set for the special case in which pi -p2- 1, m- 10, xL- 2, and TH -5 and explain your derivation (much as I did in class

Answer 1

Given that

Price of good 1=p₁

Price of good 2=p₂

Quantity of good 1=x₁

Quantity of good 2=x₂

Income =m

m=p₁x₁+p₂x₂

Budget line is given by

m= p₁x₁+p₂x₂

Condionds

Now suppose, $x_{1}\leqslant x_{L}$

P1 is replaced by 0.5p1

m= 0.5p₁x₁+p₂x₂

For $x_{L}<x_{1}\leqslant x_{H}$

m= p₁x₁+p₂x₂

Now suppose x1>xH

P1 is replaced by 1.5p1

m= 1.5p₁x₁+p₂x₂

Given that

Let us put p₁=p₂=1, m=10, xL=2, x_H=5

Budget line comprises of 3 parts in this problem

For, $x_{1}\leqslant 2$P1 is replaced by 0.5

m= p₁x₁+p₂x₂

10=0.5x1+x2

For $2<x_{1}\leqslant 5$

10= x₁+x₂

Now suppose x₁>5

P1 is replaced by 1.5p1

10= 1.5x₁+p₂x₂

Based upon above information, following consumption bundles are possible

x1	x2
0	10
1	9.5
2	9
3	7
4	6
5	5
6	1

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