Question

Imagine an economy in which Ricardian equivalence holds. This economy has a budget deficit of \(50,\) a trade deficit of \(20,\) private savings of \(130,\) and investment of \(100 .\) If the budget deficit rises to \(70,\) how are the other terms in the national saving and investment identity affected?

Short answer

Under the assumption of Ricardian equivalence, when the budget deficit increases from $50 to $70, the private savings will increase from $130 to $190 to maintain the national saving and investment identity. The trade deficit and investment will remain unchanged.

Step-by-step solution

1. Understanding Ricardian equivalence

Ricardian equivalence is an economic theory that suggests that a change in government tax or spending policy does not affect the overall level of national saving and investment, because individuals will adjust their spending and saving behavior in anticipation of future tax changes. In this exercise, we assume that Ricardian equivalence holds.

2. National saving and investment identity

The national saving and investment identity is given by: \( S_{private} + S_{government} = I + NX \), where \(S_{private}\) denotes private savings, \(S_{government}\) denotes government savings (which is equal to the budget surplus or deficit), \(I\) denotes investments, and \(NX\) denotes net exports (exports minus imports). However, as we have a trade deficit, there are more imports than exports. Therefore, NX is negative in our case.

3. Evaluate the initial values

Given the initial values of the budget deficit, trade deficit, private savings, and investment: - Budget deficit: \(-50\) (negative because it’s a deficit) - Trade deficit: \(-20\) (negative because it’s a deficit) - Private savings: \(130\) - Investment: \(100\) Using the national saving and investment identity, we can write: \[\] \(130 - 50 = 100 -(-20)\) \[ = 100 + 20.\]

4. Adjust the budget deficit

Now, let's examine the situation when the budget deficit rises to \$70. The new budget deficit value: - New budget deficit: \(-70\)

5. Analyze the effect of the budget deficit on other terms

Under the assumption of Ricardian equivalence, the increase in the budget deficit will not affect the overall level of national saving and investment. Since the budget deficit increased, we can expect an increase in private savings to offset this change. We will rewrite the national saving and investment identity equation with the new budget deficit: \((S_{private}^{new}) - 70 = 100 + 20\) To find the new value of private savings, we can rearrange the equation and solve for \(S_{private}^{new}\): \((S_{private}^{new}) = 100 + 20 + 70\) \((S_{private}^{new}) = 190\)

6. Conclusion

Under the assumption of Ricardian equivalence, when the budget deficit increases from \(50 to \)70, the private savings will increase from \(130 to \)190. This increase in private savings will offset the change in the budget deficit, maintaining the national saving and investment identity. The trade deficit and investment will remain unchanged.