i Two firms A and B simultaneously choose how much money X A and xb (in $1000s) to invest in recruiting at Kelley. The probability that firm i hires a student is Pri = Xi+xj XB O each firm is able to hire with a 50% chance. A student that is hired brings $36K in net profit (inclusive of her salary). Both firms maximize profit. and if XA = (i) Write down each firm's profit function Ti(xi). (ii) Take the derivative of firm i's profit with respect to it's own investment and set it equal to zero. Do not yet rearrange the terms. (iii) Assume that in equilibrium x A = x3 = x, that is both invest the same amount. Use your equation from part (ii) to solve for the equilibrium value of x. (iv) Now suppose you were to assume xA = x3 = x before taking the derivative of the profit function. Show that you would arrive at a different answer. Show that this answer is not a Nash equilibrium. Argue in words why not. i Two firms A and B simultaneously choose how much money X A and xb (in $1000s) to invest in recruiting at Kelley. The probability that firm i hires a student is Pri = Xi+xj XB O each firm is able to hire with a 50% chance. A student that is hired brings $36K in net profit (inclusive of her salary). Both firms maximize profit. and if XA = (i) Write down each firm's profit function Ti(xi). (ii) Take the derivative of firm i's profit with respect to it's own investment and set it equal to zero. Do not yet rearrange the terms. (iii) Assume that in equilibrium x A = x3 = x, that is both invest the same amount. Use your equation from part (ii) to solve for the equilibrium value of x. (iv) Now suppose you were to assume xA = x3 = x before taking the derivative of the profit function. Show that you would arrive at a different answer. Show that this answer is not a Nash equilibrium. Argue in words why not