The big pharmaceutical company AstraVenera released its globally patented covid vaccine on early 2021 in two bordering, but sharply different countries: Haiti (HA) and Dominican Republic (DR), with a strict ban on cross-border sales agreed with the Haitian government. The respective demand functions (in million units) for both countries are: QHA=10-PHA QDR=17-0.5PDR The total cost (TC), in millions too, depends on the total amount of units produced Q = QDR + QHA and also includes 30 million of fixed costs. TC follows the expression: TC=30+2Q+Q2/8 1. ii. What should he Actrall well as the amount of 6) iii. iv. Soon beginning to suspect of rampant corruption within the Haitian government -some officials keeping whole vaccine pallets for themselves to sell illegally to wealthy Dominicans, AstraVenera considers investing in additional security at the border to prevent cross-country sales. How much at most should AstraVenera invest on that? (25%) V. Following from AstraVenera's optimal decision in iv), now assume a second competitor, Pfizoll, with their own patented covid vaccine, enters the relevant market so it becomes a duopoly. The two brands of vaccine are considered homogeneous by the buyers so the two companies will split the demand and charge the same price, competing only on market share. If Pfizoll's total cost function is TC=30+20+Q?/20, determine the optimal quantities and market shares for both companies. (10%) vi. Explain what would happen to the market as described in v) if it was suddenly discovered that 50% of the vaccines supplied by both companies have reduced efficacy. Buyers, which are risk-neutral, cannot tell the good vaccines from the bad ones and their demand for reduced-efficacy vaccines is QDR=5-0.5PDR. (10%)