Consider the Solow model with an aggregate production function Y = AKL12 with 01, a depreciation rate and a saving rate is s. Besides technology,...

Consider the Solow model with an aggregate production function Y = AKαL1−2α with 0<α<1, a depreciation rate δ and a saving rate is s. Besides technology, A, all other factors of production can change. (Make sure to show all your work!)

1. Does this economy have increasing, decreasing or constant returns to scale?
2. What is the per capita form of the production function?
3. Find the steady-state levels k∗ and y∗. How does y∗ depend on the size of the labor force? Why?
4. Now think of the production function Y = AKαL1−2αXα where X represents land. Does this economy have increasing, decreasing or constant returns to scale? What is the per- capita form of the production function? (Hint: define x=X/L.) What if X is fixed?