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- (a) Suppose we have preferences U(X, Y) = 10X²/³ Y¹/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). < (d) What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain.< (e)_From (d) we can show that optimal demands are: X=½ M/PX and Y = ½ M/Px. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands (X*, Y*) and utility if Px = 10, Px= 5 and income M = 1200. < (f)_Suppose Px falls to Px = 8 but Py and M are unchanged (Px = 5 and M = 1200). Calculate the new optimal demands…4We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactlyonce. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)
- solve g, h please Thank youWe claimed in the text that if preferences were monotonic, then a diag-onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)12 2 4 6 8 Water (bottles per day) The figure above shows three of a consumer's indifference curves. Which point is most preferred? Point Conly Point Gonly Point Jonly Points Cand G are tied for the most preferred. More information is needed to determine which point is most preferred. 2.
- Consider the following indifference curves. U1 U2 X U3 Which indifference curves violate the assumption of monotonicity? b₁ U4T/F Explain If preference is monotonic but not strongly monotonic, indifference curves are upward sloping but may have flat portions.if the total utility of consuming the first three pieces of pizza were 50,80, and 95 respectively , the marginal utility of the third silce of pizza is?
- Given this preference relation, draw an indifference curve. xy x1 + x2 ≥ Y1 + Y2.Linda loves buying shoes and going out to dance. 20 Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is: 18- 16- U(S, T) = 2ST 14- It costs Linda $75 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $750 to spend on shoes and dancing. E 12- 1.) Use the line drawing tool to draw Linda's budget line. Properly label this line. 10- 2.) Use the point drawing tool to locate Linda's optimal consumption bundle. Label this point 'R'. 8- 6- Carefully follow the instructions above, and only draw the required objects. 4- What is Linda's marginal rate of substitution? -. (Enter your response as an 2- integer. Note that the minus sign is already included.) 0- 12 10 Shoes (S) 14 16 18 20 React tv MacBook Air 80 DII F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 @ 23 2$ & 1 3 4 7 8 Q W E T Y { A S F H. J K C V M. く tion command command option ピ ーの Dancing (T) コ B. レ1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion, determine the Marginal Rate of Substitution between X1 and X2 and the equation for an indifference curve through the consumption bundle (100,100) (solve for X2 on the left hand side of the equation). State 1 is the bad outcome that occurs with probability 0.2 and State 2 the good outcome that occurs with probability 0.8. Graph these indif- ference curves and comment on what you see. Is a consumer with these preferences risk averse, risk neutral, or risk loving? (a) V(X) = InX (b) V(X)= VX (c) V(X)= X (d) V(X)= X²
