Question

In an economy, the desired consumption and investment functions are given by,

Cᵈ = 5000 + 0.25Y - 5000r
Iᵈ= 2500 - 5000r
where Y is output and ri s the real interest rate.
Government purchases,
G = 2000.
Determine the equation for the national saving function to show how desired national saving, Sᵈ, depends on r and Y.
Sᵈ₁= __+___Y+___r.

Answer 1

`\[Sᵈ₁ = 7500 + 0.25Y - 10000r\]` the desired consumption function (Cᵈ = 5000 + 0.25Y - 5000r), government purchases (G = 2000), and assuming no taxes (T = 0), the equation becomes: Sᵈ₁ = Y - (5000 + 0.25Y - 5000r) - 2000, which simplifies to Sᵈ₁ = 7500 + 0.25Y - 10000r.

Explanation:

The national saving function (Sᵈ₁) represents the difference between income (Y) and desired consumption (Cᵈ) and government spending (G). The formula for national saving is Sᵈ₁ = Y - Cᵈ - G. Given the desired consumption function (Cᵈ = 5000 + 0.25Y - 5000r), government purchases (G = 2000), and assuming no taxes (T = 0), the equation becomes: Sᵈ₁ = Y - (5000 + 0.25Y - 5000r) - 2000, which simplifies to Sᵈ₁ = 7500 + 0.25Y - 10000r.

This equation demonstrates that desired national saving is positively related to income (Y) and negatively related to the real interest rate (r). Higher income leads to greater saving, while higher real interest rates tend to reduce saving due to the cost of borrowing.

This equation reflects the Keynesian theory where desired saving is influenced by income and interest rates. As income rises, households tend to save more, while higher interest rates encourage individuals to save less and spend more due to the increased cost of borrowing. Therefore, the national saving function, Sᵈ₁, illustrates the relationship between desired saving, income, and real interest rates in an economy.