For this assignment we consider the following market. Market demand is P = 10 Q. There are two rms, D and E. Both have cost functions TO, ((1,) = 3 + 2 - q,-. For the sake of simplicity, we restrict the output choices of the rms as follows. Firm D may choose either (I?) = 8 or q = 12. Firm E may choose either q}; = 8 or if = 6. a) Find the market price for each of the four possible output combinations. b) Find the prots received by each rm in each of the four possible output combinations. 0) Draw a normal form game for players D and E. Each player has his allowable outputs as strategies, and payoff equal to the prots derived above. (:1) Solve the normal form game for the Nash equilibrium. e) Can you identify a relationship between the two strategies for rm D? If so, what is it? f) Now construct a \"choosing the game\" game in which rm D has a chance to prepay the production costs up to q units of output. That is, rm D is effectively choosing between two costs functions T0?)(qD) = 3 + 2 - 9'1) and TCb(qD) = 27. Firm E's cost function remains as Specied above. In the second stage, rms D and E choose output simultaneously. Draw this game. g) Solve this game. h) Compare the equilibrium outcomes found in parts ((1) and (g). Which outcome does rm D prefer? Which outcome has higher consumer surplus? Explain. Which outcome has higher total welfare? Explain. i) We can think of prepaying variable costs as a somewhat limited method for committing to a given output. With this in mind, briey explain your answers to parts (h) within the context of our discussion in class regarding welfare consequences in a dominant rm model