,, solve this kindly

\f3- (25 points) Consider the utility function that shows what combinations of apples (A) and bananas (B) provide the level of utility D: -In A + =In B = 0, where O is a given level of utility. The indifference curve associated with this function reflects the levels of A and B that yield a constant level of utility. a) Derive an equation for the slope of an indifference curve associated with this utility function. Which theorem you will use? When A=6 and B=2, what is the slope of a line tangent to this indifference curve? What is the slope of the line when A = 3 and B = 14? (15 points) b) Find the MRS for both A, B pairs in part (b). (10 points)(6) The inverse market demand curve for a good is given by P(Y) = 200 - Y. (a) Suppose that there is only one firm operating in the market, with costs c(y) = y + y'. Label by yar the quantity produced. What is the quantity produced? The price? The profit? (b) Suppose that two firms operated in the market who choose their quantity (as in the Cournot model), with costs ci(y) = y + y' and cz(y) = 3y. Label by y1 and y2 the quantity produced by each firm. What is the reaction function of Firm 1? How about firm 2? PROBLEM SET 5 3 c) What is the quantity produced by each firm in the Cournot-Nash equilibrium? What is the final price? d) For the Cournot case, draw the two reaction curves and indicate the equilib rium point on the graph below. e) Can the firms increase their profits by colluding? What would happen to the market price? For this part assume that they can collude, i.e., don't worry about this being an equilibrium or not. (f) Is the possibility of colluding an equilibrium? If so, why? If not, why not? Elaborate.