budget constraint

[ranjankumarnayak5]

The Consumption basket of a consumer has two goods, X and Y. If he spends the entire
lncome on these two goods, he can buy 4 units of X and 6 units of Y; or he can buy 12 units
of X and 2 units of Y. If he spends his entire income on X alone, what is the number of units
of X that he can buy?
(A) 7
(B) 8
(c) 16
(D) 15

[SM]

Hi,

For this the answer will be 16.

here, let the income be M. Given, X=4,Y=6 and X'=12 and Y'=2,
The quantities are given to us, equating the two budget constraints (since the income (M) is same) we have: (px and py are prices of X and Y)

4px+6py=12px+2py
4py=8px
py=2px

Thus, the price of y is twice that of x.

px=1 (from above calculations), py =2

Since income is 16 (4*1+6*2), at y=0, we will consume, M/px= 16 units of X

[Nikkita]

Yes answer=16

4x+6y=M
12x+2y=M
 Solving both equations, we get x=M/16, y= M/8

So, if spend money on x alone, then x= M/(M/16)= 16 units ans.

[ranjankumarnayak5]

Thanks a lot.SM.

[ranjankumarnayak5]

Thank you Nikkita.