Consider the following highly stylized model on price competition. Suppose there are only two supermarkets in Australia: Coles and Woolworths, and they sell only one product: milk. Let us further assume that after graduating from Deakin, you work at Coles as a business analyst, and you are in charge of its pricing strategy. Based on historial sales data, you estimate the demand function of Coles milk is QC(PC, PW) = 7.6 - 10PC + 8PW where PC is the price of Coles milk and PW is the price of Woolworths milk. You view Woolworths as an equivalent rival of Coles. Accordingly, you estimate the demand function of Woolworths milk is QW(PC, PW) = 7.6 - 10PW + 8PC. Coles faces the following total cost function TC(QC) = (FMP + V)QC + 1, where FMP represents the average farmgate milk price (the wholesale cost of milk before process- ing) and V represents all other variable costs per unit. Similarly, you estimate that Woolworths faces the following total cost function TC(Q ) = (FMP + V)Q +1. Suppose currently we have FMP = $0.54 and V = $0.26. Each firm chooses one of the following two price points for its milk: $1.3 or $1.5. Your objective as a Coles business analyst is to set the price of Coles milk correctly to maximize Coles' profits. Question 1: Construct the payoff matrix for this pricing game. Question 2: Suppose Coles and Woolworths set their prices simultaneously and independently. Find all Nash equilibria of this game. Based on the notion of Nash equilibrium, determine the price point you should set for Coles milk. Explain. Question 3: Based on your answers in (a)-(b), discuss whether the price competition between Coles and Woolworths is strategically equivalent to the prisoner's dilemma. If Coles and Woolworths are able to agree on playing the "best" equilibrium (from the firms' perspective), what would be the price set by each firm? Question 4: Suppose the firms move sequentially: Coles sets its milk price first, and after observing the price set by Coles, Woolworths sets its milk price accordingly. Draw a game tree and find the SPNE of this sequential move game. Suppose due to inflation FMP increases from $0.54 to $0.71, and V increases from $0.26 to $0.33