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The Intertemporal Budget Constraint c1 c2 m2/p2 m1/p1 0 0 Saving Borrowing Slope = Price Inflation Define the inflation rate by p where For example,p = 0.2 means 20% inflation, andp = 1.0 means 100% inflation. Price Inflation We lose nothing by setting p1=1 so that p2 = 1+ p . Then we can rewrite the budget constraintas Price Inflation rearranges to so the slope of the intertemporal budgetconstraint is Price Inflation When there was no price inflation (p1=p2=1) the slope of the budget constraint was -(1+r). Now, with price inflation, the slope of the budget constraint is -(1+r)/(1+ p). This can be written asr is known as the real interest rate. Real Interest Rate gives For low inflation rates (p ? 0), r ? r - p .For higher inflation rates thisapproximation becomes poor. Comparative Statics The slope of the budget constraint is The constraint becomes flatter if the interest rate r falls or the inflation rate p rises (both decrease the real rate of interest). Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = The consumer saves. Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = The consumer saves. An increase in the inflation rate or a decrease in the interest rate “flattens” the budget constraint. Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = If the consumer saves thensaving and welfare are reduced by a lower interest rate or a higher inflation rate. Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = The consumer borrows. Comparative Statics c1 c2 m2/p2 m1/p1 0 0 slope = The consumer borrows. Afall in the inflation rate or a rise in the interest rate
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