Question 1 [10 marks]
Consider a twoโperiod economy with a household and government.
The household behaves according to its intertemporal budget constraint, but faces a borrowing constraint that prevents periodโ1 consumption from exceeding periodโ1 disposable income, which can be written as follows,
Here ๐ถ is consumption, ๐ is taxation, ๐บ is government expenditure, and ๐ is the real interest rate. Subscripts denote periods 1 and 2.
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You may assume that household and government face the same real interest rate, ๐. Further, suppose that the household has a preference for consumption today, such that its borrowing constraint is binding, forcing it to consume its periodโ1 income today and periodโ2 income tomorrow. That is to say, initially ๐ถ1 = (๐1 โ ๐1) and ๐ถ2 = (๐2 โ ๐2).
This situation is shown in the following diagram.
Now consider a situation where the government tries to stimulate the economy via a tax cut in period 1. The government maintains expenditure in each period at ๐บ1 and ๐บ2, but it cuts taxes to ๐1โฒ in period 1 and consequently increases taxes to ๐2โฒ in period 2, to still obey its intertemporal budget constraint.
Is the fiscal policy via the tax cut effective at stimulating periodโ1 consumption? Draw a diagram and provide clear explanation about how this example relates to Ricardian Equivalence.
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