Supply and demand for a perfectly competitive industry areQ d​ =a+bP+cP,P r​ is the price of a related good,Q s​ =d+eP+fU,Uis the wage of union workers in the industry. a. For each parameter a-j indicate relevant bounds (e.g., real positive, or<1and>0) and explain why. b. What is equilibrium price in the industry? Use the letters or values you choose for parameters c. Consider a firm in this industry. The AVC curve isAVC=.g+hQ+iQQ 2 +jP. What would the ATC curve be? Identify any new variable you add to AVC. d. Given the AVC and ATC, what would be the values of the parameters in the AVC and ATC curves if there are short term excess profits? e. Values of the parameter if in the short run the firm has losses but continue to operate? f. Values of the parameter if in the short run the firm is forced to shut down? g. Values of the parameter if in the short run the firm is making normal profits?

a. The parameters a, b, c, d, e, f, g, h, i, and j are all real numbers. The parameters a and d are the intercepts of the demand and supply curves respectively and can be any real number. The parameters b and e are the slopes of the demand and supply curves respectively and should be positive for a normal good. The parameters c and f are the effects of the price of a related good and the wage of union workers on demand and supply respectively and can be any real number. The parameters g, h, i, and j are the coefficients of the AVC curve and can be any real number.

b. The equilibrium price in the industry is found by setting the quantity demanded equal to the quantity supplied and solving for P. That is, a + bP + cPr = d + eP + fU.

c. The ATC curve would be AVC + (Fixed Costs/Q). The new variable added to AVC is Fixed Costs, which represents the costs that do not change with the quantity of output produced.

d. If there are short term excess profits, the AVC would be less than the price and the ATC would be less than the price. This implies that the parameters in the AVC and ATC curves would be such that AVC < P and ATC < P.

e. If in the short run the firm has losses but continues to operate, the AVC would be less than the price but the ATC would be greater than the price. This implies that the parameters in the AVC and ATC curves would be such that AVC < P and ATC > P.

f. If in the short run the firm is forced to shut down, both the AVC and the ATC would be greater than the price. This implies that the parameters in the AVC and ATC curves would be such that AVC > P and ATC > P.

g. If in the short run the firm is making normal profits, the AVC would be less than the price and the ATC would be equal to the price. This implies that the parameters in the AVC and ATC curves would be such that AVC < P and ATC = P.