More BC confusion

[ascapa]

(1) P.J. is trying to decide how much to consume in time periods 1 and 2, (c₁, c₂). He will get $100 in period 1 and $100 in period 2. He can save and borrow as much as he wants between the two time periods at an interest rate of 20%. If P.J.’s utility function is  u(c1,c2)=c1c2, what level of consumption does he choose in period 2 if the inflation rate is also 10%? Assume that p₁ = $1.

              (a) 100

              (b) 140

              (c) 180

              (d) 80

              (e) None of the above

When I use the real BC: (1+p)c1+c2=(1+p)m1+m2, I can't get the right answer. Does anyone have work for this? The answer is supposed to be 100.

[J]

Actually, I think there might be a typo here, because when it says "the inflation rate is also 10%" the word "also" implies that it would be the same as the interest rate. I believe that the inflation rate that is supposed to be "also 20%", in which case (1+p) would just be 1 and you would get 200.

I'm sure you got something like 1.09 for your 1+p, correct? I got the same thing when I did 1.2/1.1.

c2 = m1/2 * (1+p) + m2/2

m1 = 100

m2 = 100

50*(1+p) + 50

(1+p) = (1+r)/(1+pi)

r = .1

pi = .2

1+p = (1 + .1) / (1 + .2) ~= 1.09

50*(1.09) + 50 = 104.5

if pi = .1, 1+p = 1.1/1.1 = 1

50(1) + 50  = 100

[ascapa]

The reason I don't think it's a typo is because when solved using the nominal method, you can get the answer of 100. I don't know how I am supposed to know to use the nominal method on this problem though.

[J]

I don't think of it is "nominal method" so much as nominal terms. If you're given the inflation rate you have to use it. Plus the fact that it's mentioned in the question of the problem implies that inflation has to be taken into account here. If the inflation rate isn't given or is given as 0 then you could do it in nominal terms or the 'method' as you describe. 

When you see the problem, ask yourself these questions:

• Do I see a [nominal] interest rate? (You should every time)
• Do I see an inflation rate? If no, then use (1+r). If yes, then use (1+p). If inflation is zero, use (1+r). 
• Recall that 1+p = 1+r/1+pi.
• Dividing by 1+p (as in the present value constraint) is the same as multiplying by the inverse: 1/1+p = (1+pi/1+r)