Question

True or False. The production function f(x,y)=x^(2/3)+y^(2/3) has increasing returns to scale

Answer 1

Answer: True

When all the inputs are increased at a specific amount, the output increases more than the increase in inputs, the production function shows increasing returns to scale.

f(X,Y)=X^2/3+Y^2/3

Let, us denote f(X,Y) = Q , i.e., production or quantity of output.

Now, let us increase both the inputs X, and Y by ''. For the increase in inputs, let the output, Q changes to 'Q^*'.

So, Q^* = (X)^2/3 + (Y)^2/3

Or, Q^* = ^{2/3 + 2/3} * (X^2/3+Y^2/3)

Or, Q^* = ^4/3 (X^2/3+Y^2/3)

Or, Q^* = ^4/3 * Q

4/3 1 ,

The the quantity or output increases more than the increase in inputs, X, and Y.

Now, as the proportionate increase in the quantity of output is greater than the proportionate increase in inputs, the production function here exhibits increasing returns to scale.

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