Question

10. Assume that a country produces an output I of 50 every year. The world interest rate is 10%. Consumption C is 50 every year, and I = G = 0. There is an unexpected drop in output in year 0, so output falls to 28 and is

Answer 1

Solution:

10. The new level of consumption be from then on is:

We know , output (Z) = C+ I + G + X , where X is export minus import
When Consumption is 50 and Z is also 50
We have , 50 = 50 + I+G
=> I+G = 0
=> Left hand side = right hand side
Now, output is 39 but the consumption is 50
=> 28 = 50 +I+G (I+G= 0)
=> 28 is not equal to 50
So, to meet the consumption of 28 we need extra 50-28 = 22 quantity of output.
Therefore, the present value of consumption PV(C) is PV(Q) - PV(G) = 28 +50/0.10 = 528
In order to determine level of consumption for each period, we know that the country will try to maintain the given level of consumption:-
i.e. PV(C) = C + C/r^*   
=> 528 = C+ C/0.10
=> C = 48
So, as the output drops to 28 in the year 0 , the country must burrow 20 units in the period 0 to consume 48 units as for every 20 units consumed the consumption level goes down by 2 unit i.e. NFIA= 20*0.1 = 2 unit in subsequent periods.So, we can say C= 48 units in period 0 and the change in consumption/ new level of consumption can be calculated as :-
Change in consumption = r^* /(1+r^*) * Change in quantity = 0.10/(1+0.10) * (-22) = -2
Hence, consumption decrease by 2 unit to C= 48 units