Consider two chemicals producers selling a differentiated product. Assume firm A has a global branding like DuPont. Firm B is a run-of-the-mill seller, Joe's Chemicals. Due to differences in attributes and quality between firms A and B, consumers perceive the two firms as different, affecting the demand for their products. Finally, due to differences in quality control and process related expenditures, the firms have differential costs. The two firms' demand and costs are: (1) QA = 100 - 4PA + 3Pg (2) TCA = 5QA (3) QB = 70 - 6PB + 2PA (4) TCB = 4QB (1) (5 points) Derive the firms' pi Multilevel List unctions from the demand and cost information. Show the derivation steps. Calculate the firms' equilibrium prices, quantities, and profits. Firm A: Qa= 100 - 4Pa+3Pb IC 5Qa -> MC = $5/unit II=(Pa-5)(100-4Pa+3Pb) -> 120 -8P. + 3Pb =0 Pa = 15 + .375Pb Firm B: QR = 70 - 6Pb+2Pa IC 40 -> MC= $4/unit II=(Pb-4)(70 -6Pb+2P.) -> 94 - 12Pb +2P. =0 Pb = 47/6+1/6P Equilibrium Prices: Pa = 15 +.375(47/6 + 1/6P.) = $19.13/unit Pb = 47/6 +1/6(15+.375Pb) = $11.02/unit Equilibrium Quantity: Q=100 -4(19.13) + 3(11.02) = 56.54 units - QR =70-6(11.02) + 2(19.13) = 42.14 units Profit: I. (19.13-5)(100 - 4(19.3) + 3(11.02)) = $798.80 I (1 1.02 -4)(70 -6(11.02) + 2(19.13)) = $295.83(2) (4 points) Now consider an environmental regulation where both firms must reduce effluent discharge. Firm A being more advanced with better process controls, experiences a 20% increase in its MC. Firm B, on the other hand, faces a 100% increase in its MC. Re-solve the problem to derive (show the steps) the two firms' price response functions. Calculate the firms' equilibrium prices, quantities, and profits. Firm A: Q= 100 - 4Pa+3Pb TO 5Qa -> MC = $6/unit (20% increase) - II=(Pa-6)(100-4Pa+3Pb) -> 124 - 8Pa+3Pb= 0 Pa = 15.5+.375Pb Firm B: Multilevel List Qa = 70 - 6Pb+2Pa TC 4Q -> MC=$8/unit (100% increase) II=(Pb - 8)(70 - 6Pb+2P.) -> 112 - 12Pb +2Pa = 0 Pb = 28/3+1/6Pa Equilibrium Prices: Pa = 15.5 +.375(28/3 + 1/6P.) = $20.26/unit Pb = 28/3 +1/6(15.5+.375Pb) = $12.71/unit Equilibrium Quantity: Q= 100 -4(20.26) + 3(12.71) = 57.09 units QR = 70 -6(12.71) + 2(20.26) = 34.26 units Profit: I (20.26 - 6)(100 - 4(20.26) + 3(12.71)) = $814.10 - I (12.71 -8)(70 -6(12.71) + 2(20.26)) = $161.36