Constant Returns to Scale in a Closed Economy: Analysis of Production Function Yt = 0.2√(Kt)^2 + (Lt)^2

To verify if the aggregate production function has constant returns to scale, we need to check if doubling the inputs (capital and labor) results in a doubling of output.

Let's consider the production function Yt = F(Kt, Lt) = 0.2√(Kt)^2 + (Lt)^2.

To check for constant returns to scale, we need to compare the output when the inputs are doubled to the output when the inputs are not doubled.

Let's consider the case where the inputs are not doubled:

Yt = F(Kt, Lt) = 0.2√(Kt)^2 + (Lt)^2

Now, let's consider the case where the inputs are doubled:

Yt' = F(2Kt, 2Lt) = 0.2√(2Kt)^2 + (2Lt)^2 = 0.2√4(Kt)^2 + 4(Lt)^2 = 0.2 * 2 * √(Kt)^2 + (Lt)^2 = 0.4√(Kt)^2 + (Lt)^2

Therefore, Yt' = 0.4Yt.

Since Yt' is double the value of Yt, the production function has constant returns to scale.