Please explain if the following statement is true or false: “In the endowment economy model reviewed...

Please explain if the following statement is true or false: “In the endowment economy model reviewed in Chapter 3 of the textbook, if the household’s initial asset position is positive, (1 + r0)B0∗ > 0, then the initial endowment (Q1, Q2) is located below the intertemporal budget constraint and this in turn implies that it is feasible (affordable) for the household to consume its endowment in each period; C1 = Q1 and C2 = Q2.”. Use the equation and the graph of the intertemporal budget constraint to support your answer (with C2 on the vertical axis and C1 on the horizontal axis).

please explain

Solutions

Expert Solution

Consider the given problem here an individual having initial endowment (Q1, Q2) and the initial asset position is also positive. So, the budget constraint of each period is given below.

=> C1 = Q1+ B0*(1+r0) - S, for period 1, where “S=savings or lending”.

=> C2 = Q2 + S*(1+r), for period 2.

So, the intertemporal budget line is given by.

=> C2 = Q2 + S*(1+r), => C2 = Q2 + (1+r)*[Q1 + B0*(1+r0) – C1].

=> C2 = Q2 + (1+r)*[Q1 + B0*(1+r0) – C1], => C2 = Q2 + (1+r)*Q1 + (1+r)*B0*(1+r0) – (1+r)*C1.

=> (1+r)*C1 + C2 = Q2 + (1+r)*Q1 + (1+r)*B0*(1+r0).

=> C1 + C2/(1+r) = Q2/(1+r) + Q1 + B0*(1+r0), be the intertemporal budget line of the agent. Now, at the endowment point “C1=Q1” and “C2=Q2”. The LHS of the equation is “C1 + C2/(1+r) = Q1 + Q2/(1+r)”, and the RHS of the above equation is “Q1 + Q2/(1+r) + B0*(1+r0)”. If we compare the LHS with RHS we can see that LHS is less than RHS, => initial endowment is affordable.

Here the intertemporal budget constraint is AB, and all the points below the budget line is affordable by the individual. So, here “E” be the endowment point which is also affordable.

*THANK YOU

Rahul Sunny answered 1 year ago

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