Reservation price

[Amita_IITM]

The only quantities one can buy are 1 unit or 0 unit. For x1=0 and all positive values of x2, U= (x1+4)(x2+2). If income is 28, what will be the reservation price for good1.

Please help me with the method.
Thank you.

[Arushi :))]

Reservation price is the  price at which the consumer is indifferent between buying and not buying the good.
So, U (0,x2) = U (1,x2)
Now , there is nothing mentioned about price of the good 2,
we can assume that its the consumption of all other goods
and assume price of good 2 be equal to 1.
this means that whatever amount the consumer consumes of all other goods equals the amount spent by him on all other goods.
U(0, x2) = (0+4)(x2+2)
x2= M-money spent on good 1 = M-0 = M
U(0,x2) = 4(M+2)
similarly
U(1,x2) = (1+4)(x2+2)
x2 = M - money spent on good 1
= M-p1*1
U(1,x2) = 5( M-p1+2)
equating the two utilities,
we get 5p1= M+2 = 30
This gives p1 as 6.
:)

[Amita_IITM]

Thank you so much Arushi :)

[Ashima]

I didn't understand it from this part: U(1,x2) = 5( M-p1+2)
equating the two utilities,
we get 5p1= M+2 = 30
This gives p1 as 6.

Please could u explain again. :(

[Amita_IITM]

Ashima,
Pur m=28, as income is given as 28. You will get 6. :)

[Gayyam]

Thank you Arushi! That was great. :)