Question

Consider an economy with Cobb-Douglas aggregate production function given by Y = (AK^1/4)(L^3/4) where A stands for TFP, K for capital and L for labor.

1. Prove that this production function exhibits constant returns to scale.

2. Solve for the MPK and MPL.

3. Prove that this function exhibits diminishing MPK and diminishing MPL.

4. Assume now that the production function is given by Y = (AK^α)(L^β)(Z^γ), where Z represents an amount of land employed in the production. Under what condition is this function constant returns to scale?

Answer 1