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Problem 3 Short Run decisions at the Firm Level Consider a perfectly competitive rm that can produce birthday hats using labor and (L) and equipment (K). The rm's Weekly production function is q = 20L1/2K1/3. a) Does the production function displays diminishing marginal returns? Do you expect this rm's short run marginal cost to be increasing or decreasing? Explain. At the start of the year the firm signed a contract for 8 pieces of equipment. In the short run, equipment is a xed input and its cost is sunk. b) Find the rm's short run conditional demand for labor LASR = L(q). The daily cost of labor is 3540 While the daily cost of equipment is 1550. c) Find the rm's short run total cost function TC(q). What is xed cost FC and What is variable cost VC (q) at this rm? d) If the rm can sell its output at a unit price of $4, what is the rm's prot maximizing output? :11) Find what output the rm would produce is open d2) Find the rm's prot if producing this level of output d3) Is the rm earning a prot, breaking even or incurring a loss? d4) Should the rm shut down? e) In a graph where you measure quantity (q) along the horizontal axis, draw the rm's marginal cost, average cost and average variable cost. Then, adding a price line, illustrate the rm's prot maximizing output. f) Suppose government introduces a $2 per unit tax. How does this affect the firm's marginal cost? How does it affect the firm's optimal level of output? Illustrate in a diagram. g) Suppose government introduces an $80 licensing fee. How does this affect the rm's marginal cost? How does it affect the rm's optimal level of output? Illustrate in a diagram. h) Which policy raises more revenue