If you can answer all 4 parts that would be greatly appreciated!

Consider an economy in which the production function of the representative firm is given by Y = zF(K, N), with F(K, N) = K1/2 + N 1/2 2 , and z = 0.5. Assume h=24 and the firm commits to pay a wage rate w = 1.5 to the worker for each unit of time worked.

1. Does the production function have the constant returns to scale property?

2. Assuming the firm operates with a capital K=1.5 in the short run, does the production function display the law of decreasing marginal product?

3. Find the optimal demand for N.

4. Assume the government decides to prevent any firm from polluting. The firm discovered that polluting can be avoided at a cost of 0.25 units of output per unit of output produced. To reduce the cost of reducing pollution, the government decides to pay the firm a given amount s for each hired worker. Calculate the s that will incite the firm to hire the number of workers found in Question 3 assuming w = 1.