Question

PLEASE HELPPPPPP

4. Consider a world with two goods as above, good 1 and good 2. In this case assume that the per unit prices are fixed as pi,p2 > 0 and income at m > 0. However, there are two wrinkles. First, there is a fixed cost k > 0 involved in receiving any strictly positive amount of good 1. In addition there is rationing of good 1, so that no more than xH > 0 is available at any price. Graph the budget set for the special case in which P1 P2 1, m = 10, k = 2, and XH 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

Fixed cost in receiving good 1=k

Total expenses will be at most equal to m

m=(k+p₁x₁)+p₂x₂

Budget line is given by

m=k+p₁x₁+p₂x₂

where x₁<=x_H and k=0 for x₁=0

Let us put p₁=p₂=1, m=10, k=2, x_H=5

10=2+x₁+x₂

8=x₁+x₂

Budget line is given by

$x_{1}&plus;x_{2}=8\, \, for x_{1}>0, x_{1}\leqslant 5$ -----------------(1)

and

$x_{2}=10\, \, \, for x_{1}=0$ -------------(2)

(Note: if consumer decides not to buy x1, he can buy 10 units of x2 as shown by equation 2. If he decides to buy some quantity of x1, fixed cost will be incurred and consumption can be determined with the help of equation 1. It should also be noted that consumer cannot buy more than 5 units of x1)    

Let us make the choice bundle subject to income constraint

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