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Answer all parts. Consider two economic agents 1 and 2. Agent 1 determines the quantity of good .r and agent 2 chooses an amount of good y. The utility of agent 1. Ui(x. y. a), is affected not only by his own consumption of goods .r, but also by agent 2's consumption of good y and the structure of t externalities between the agents also depends on the 'social parameter"a'. Symmetrically. t he utility of agent 2, 112(x, y. a). is affected not only by his own constunption of goods y, but also by agent l's constunption of good z. Assume the above scenario when the utility maximization (first-order conditions) of each agent 1 and 2 generates the following system of implicit functions 
F, (r, y, a) = .r2 — ay2 = 0, F2(x. y. a) = a.r2 + y2 = 0. 
a. Can we find an point (x', y) tow (0, 1) so that (4 a) satisfies these two equations if we change the parameter by a magnitude da to a' near a = 2 around the points (x = 1, y = 1, a = 2) and(x= 0, y = 1, a = 2) ? (15 Marks) b. Use the Cramer's rule to evaluate the derivative 2 evaluating the change in y with respect to parameter a at the point (1,1,2) (10 Marks)

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