Problem 8 Suppose your utility function is U(xa,xb) = (xa + 2)(x + 6), where xa is the number apples and x, is the number of bananas. a) What is the

slope of your indifference curve at the consumption bundle (xa,Xb) = (4, 6)? b) Draw a line with this slope through point (xa,Xb) = (4,6). c) The indifference curve through the point (x,xb) = (4,6) goes through the points (_______,0), (7,______), and (2,_____). d) Draw the indifference curve going through all the four points./n= e) The equation for your indifference curve through the point (4,6) is x₂ = f) You currently have the bundle (x,xb) = (4,6). Your roommate wants to give you 9 bananas in return for 3 apples. Should you accept the offer? g) Mark the bundle (1,15) on the graph. i) Would you be willing to give up 2 apples for 6 bananas? Choc h) Your friend tells you, "Your marginal rate of substitution is -2, which means that for an extra apple, you should be willing to trade two bananas. I am offering 3 bananas for every apple of yours. Since I am offering more than your marginal rate of substitution, you should accept my offer." You reply, "You're right that my MRS is -2. But MRS holds only for small trades where the change in apples is small. Your offer of 9 bananas for 3 apples is too big of a trade. You see, my indifference curve is not a straight line." Given this conversation between you and your friend, would you be willing to give up 1 apple for 3 bananas? j) On the graph, draw a line with slope -3 through the point (4,6). This line shows all bundles that you should be willing to trade at the rate of 1 apple for 3 bananas. Label the segment of the line that represents trades that make you better of than without trade. Com