4. A Firm has the following production function: y = L(POWER)1/3 , K(POWER)1/2.

(a) Does this production function exhibit increasing, decreasing, or

constant returns to scale? Prove.

(b) Suppose in the short run, capital is .xed 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;

r; and p increase? Explain your results intuitively.

(c) Now, suppose the government decides to impose a payroll tax of

$t per worker employed. What will the e.ect be on L? Why?

(d) Alternatively, if the government decides to impose a lum-sum tax

of $T, what will the e.ect be on L? Why?