Please solve

4. A rm has the following production function:y = L\" 3K 1/ 2. (a) Does this production function exhibit increasing, decreasing, or constant returns to scale? Prove. (b) Suppose in the short run, capital is fixed at K = 100. Assuming that the output and factor prices are p, w, and r respectively, nd rm's factor demand for labor. What will the effects be when w, 7', and p increase? Explain your results intuitively. (c) Now, suppose the government decides to impose a payroll tax of $13 per worker employed. What will the effect he on L\"? Why? (d) Alternatively, if the government decides to impose a lumsum tax of $T, what will the effect he on L\"? Why