Consider the perfectly competitive market for handmade rugs. The rms in this market are identical and each has a short run total cost function equal to SRTC = 200 + 5g + 0.5q2, where q is the number of rugs a rm produces. The market price for each rug is equal to $15. Show your work to receive full credit. a) What is the equation for the rm's short-run marginal cost (SRMC) curve. Draw it on a graph with the marginal revenue (MR) curve. Calculate and mark on your graph the prot-maximizing q". b) Write the equation for the short-run average total cost curve (SRATC) and solve for its value evaluated at q" (SRATC*). Draw the SRATC and mark SRATC" on your graph from part (a). c) Write the equation for the short-run average variable cost curve (SRAVC) and solve for its value evaluated at q* (SRAVC*). Draw the SRAVC and mark SRAVC" on your graph from part (a). d) Calculate the rm's economic prot when they produce at q*. Shade the area that represents prot on the graph you drew above. e) Should this rm stay open or shut down in the short run? Explain your answer. f) Based on what you know about this market, what should happen to the number of rms in this market and what will happen to the market price in the long run? g) Calculate the long-run equilibrium price and the number of units each rm produces at that price. Mark the long-run price on the graph you drew in part (a) or draw a new graph to indicate where it is