52 CHIOICE (Ch. 5) (g) The best bundle that Charlie can afford must lie somewhere on the line you just penciled in. It must also lie on his budget line. If the point is outside of his budget line, he can't afford it. If the point lies inside of his budget line, he can afford to do better by buying more of both goods. On your graph, label this best affordable bundle with an E. This happens where IA = 20 and EB=10 Verify your answer by solving the two simultaneous equations given by his budget equation and the tangency condition. (h) What is Charlie's utility if he consumes the bundle (20, 10)? 200 i) On the graph above, use red ink to draw his indifference curve through (20,10). Does this indifference curve cross Charlie's budget line, just touch it, or never touch it? yes touch 5.2 (0) Clara's utility function is U(X, Y) = (X +2)(Y +1), where X is her consumption of good X and Y is her consumption of good Y. (a) Write an equation for Clara's indifference curve that goes through 36 - 1 the point (X, Y) = (2, 8). Y = On the axes below, sketch Clara's indifference curve for U = 36. 36 + (2 + 2 ) - 1 W Y 16 7 4 7.4 12 8 x 8 10 4 9 0 4 8 12 16 2 9 X (b) Suppose that the price of each good is 1 and that Clara has an income of 11. Draw in her budget line. Can Clara achieve a utility of 36 with 2+1 this budget ?_ yes ( 10 + 2 ) * ( #+ ) = 36NAME 53 (c) At the commodity bundle, (X, Y), Clara's marginal rate of substitut tion is (d) If we set the absolute value of the MRS equal to the price ratio, we have the equation Y+ 1 = 1 (e) The budget equation is_ xty = 11 (f) Solving these two equations for the two unknowns, X and Y, we find X = 16 and Y