In the consumption savings model suppose that we have a representative consumer
ID: 1220505 • Letter: I
Question
In the consumption savings model suppose that we have a representative consumer and his utility is given by U(c, c') = min{c, beta c'} The budget constraint for the consumer is the same as we have in the lectures. Suppose the government finances expenditures G and G' by lump-sum taxes (t > 0 and t' > 0) and borrowing, B. The form of the budget constraint is the same as in the lectures. Find consumer's consumption the first and second period. Now assume that the government decides to keep the expenditure the same but sets t = 0 to finance G and G". Keeping interest rate constant, find the amount by which tomorrow's tax will have to change in order to have the government's budget constraint hold. Show that consumer's optimal consumption choice is still the same as before after the tax change in (b). Find the amount of consumer savings before and after the tax change in (b). Does saving go up or down after the change?Explanation / Answer
Here
U = min (c, Bc') and
budget constrait is c + c'/(1+r) = y + y'/(1+r) - t - t'/(1+r) .....[here y, y', t, t', r are fixed at a certain level]
The price ratio is 1/1+r and the consumer always consumes at c = Bc'
substituting this,
=> Bc' + c'/(1+r) = y + y'/(1+r) - t - t'/(1+r)
=> c' [B + 1/(1+r) ] = y + y'/(1+r) - t - t'/(1+r)
=> c' = [ y + y'/(1+r) - t - t'/(1+r) ]/ [B + 1/(1+r) ]
and c = B[ y + y'/(1+r) - t - t'/(1+r) ]/ [B + 1/(1+r) ]