(a)Suppose we have the following production function: Q = K3/4L1/4.Confirm the technology is constant returns to scale (CRS). Show your work and explain what it means.

(b)Now suppose K is fixed in the short-run at 21.544 (so that K3/4 = 10). Let r = $10 and w = $20. What is the firm's cost minimization problem? Explain.

(c)Derive the short-run cost function. Show that short-run costs are increasing in Q and that average variable and marginal costs also rise as Q rises. You can use math or a table/figure to do this.

(d)Suppose P = $100. What is the firm's profit maximization problem?

(e)Show that optimal Q = 23.20 in the short-run. You can use math or a spreadsheet. Also show costs, revenues, and profits. Should the firm simple choose Q = 0 and shut-down?

(f)Now let both K and L be variable. What is the firm's long-run cost minimization problem now? What two conditions must be met to ensure the firm is minimizing costs.Explain and use a diagram.

(g)We can show that the MRTS = -3 L/K. What is the MRTS measuring and why does it change along the isoquant?

(h)Let r = $10 and w = $20.Find the long-run cost function (C = wL + rK). Show that average and marginal costs are constant (eg the same value for any Q).Why is this the case?