# List of Topics and Examples
📗 Socrative Game:
(1) Cake cutting game
Choices: A = (84.4, 11.3, 3.9, 0.2, 0.1); B = (67.4, 21.5, 9.0, 2.2, -0.1); C = (55.5, 17.4, 13.5, 7.8, 5.8); D = (30.3, 20.4, 23.7, 14.1, 11.5)
Results: Morning (no Production Ex Ante: A 0%, B 9%, C 11%, D 80%) (no Production Ex Post: A 13%, B 13%, C 13%, D 63%) (with Production Ex Ante: A 65%, B 5%, C 14%, D 16%) (with Production Ex Post: A 38%, B 22%, C 16%, D 24%)
Results: Afternoon (no Production Ex Ante: A 4%, B 4%, C 13%, D 78%) (no Production Ex Post: A 12%, B 15%, C 8%, D 65%) (with Production Ex Ante: A 36%, B 0%, C 11%, D 54%) (with Production Ex Post: A 30%, B 7%, C 0%, D 63%)
Comments:
Video: Review
📗 Definitions and Theorems:
(1) Pure exchange economy; feasible allocation; Pareto domination; Pareto efficient
(2) Competitive equilibrium
📗 Algorithms:
(1) Finding Pareto set (constraint maximization method and MRS method)
(2) Finding competitive equilibrium
📗 Examples:
(1) Colored pencil example
(2) Cobb-Douglas example
📗 Problems:
File:
Questions ;
Answers.
(1) Asymmetric Cobb Douglas economy
Update July 16: Part 1 computation mistake in the last step.
(2) Double quasi-linear economy
(3) Economy with a bad good (Correction: original endowment leads to corner solutions, new endowment point added in the solution):
Video
Update July 16: Part 2 minor changes with the expression of y*.
(4) Double complement economy:
Video
(5) Double substitute economy:
Video Part I ;
Video Part II ;
Video Algebra
Update July 18: mistake in algebraic method to solve fixed
Workbook (recommended): 32.1, 32.2, 32.3, 32.4, 32.5, 32.7, 32.8, 32.10
Workbook (doable): 32.6, 32.9
# Related Questions
(27) How to draw the indifference curves from a utility function? A: Set the utility function equal to a fixed u, solve for either x or y, then draw the resulting function.
(25) When can MRS method be used? A: You can use MRS method when there won't be any corner solutions. When x = 0 and y = 0 are clearly not the optimal, for example Cobb-Douglas, then you know there won't be corner solutions.
(22) Why is the price p = -1 for the Bad Good question in the problem set? A: This is just one of infinite number of CEs. In order to have both x >= 0 and y >= 0 feasible. p = -1 is one price such that when you substitute it into the demands, you get all x_A = y_A = x_B = y_B = 0 all feasible.
(21) How to solve for the PE set for the substitute utility functions algebraically? A: Mistake in the steps are fixed now July 18. Video explanation:
Link.
(20) How to deal with max{x, y} utility functions? A: Their indifference curves are L shapes rotated 180 degrees. See video:
Link.
(14) How to solve for the PE set and CE for substitute and complement utility functions? A: See problem set: complements:
Video ; substitutes:
Video Part I ;
Video Part II
(13) Why are there two horizonal pieces in the Pareto set when both utilities are quasilinear? A: See video:
Link
(11) Can you explain the fundamental theorems again? A: Yes.
Video.
(10) How to find upper contour set on the Edgeworth box? A: See video:
Link.
(9) How to understand the numbers inside the Edgeworth box? A: They are utility of consumer A and utility of consumer B:
Video Explanation.