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9_MathematicalConstrainedOptimization_ToPost

# 9_MathematicalConstrainedOptimization_ToPost - .What...

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“What we call chaos is just patterns we haven’t recognized.   What we call random is just patterns we can’t decipher.  What  we can’t understand we call nonsense.  What we can’t read we  call gibberish.” –Chuck Palahniuk ECON 410 Constrained Optimization (Mathematical) 1 2 1 1 2 2 ( , ) ( ) U x x I p x p x λ = + - - L HW2 Long-Form on Large Table

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2 Class 9 - Constrained Optimization (Mathematical)
3 Class 9 - Constrained Optimization (Mathematical)

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4 Class 9 - Constrained Optimization (Mathematical)
5 Class 9 - Constrained Optimization (Mathematical) Constrained Optimization 1. If preferences are monotonic, then my optimal point will be on the Budget Line or else monotonicity is violated. 2. If preferences are rational, convex, and monotonic, then if I am consuming both goods, my optimal point will be on the Budget Line and will be at a point such that the slope of my indifference curve is identical to the slope of my Budget Line or a kink in the Budget Line or Indifference Curve

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6 Class 9 - Constrained Optimization (Mathematical) Constrained Optimization 1. If preferences are monotonic, then my optimal point will be on the Budget Line or else monotonicity is violated. 2. If preferences are rational, convex, and monotonic, then if I am consuming both goods, my optimal point will be on the Budget Line and will be at a point such that the slope of my indifference curve is identical to the slope of my Budget Line or a kink in the Budget Line or Indifference Curve
7 Class 9 - Constrained Optimization (Mathematical) …the slope of my indifference curve is identical to the slope of my Budget Line…

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Group-Clicker Question (P): What is another name for the slope of an indifference curve assuming x1 is on the x-axis and x2 is on the y-axis? 1 2 3 4 68% 14% 0% 18% 1. MRSx1,x2 2. MRTx1,x2 3. Ux1 4. All of the above
Group-Clicker Question (P): What is another name for the slope of the budget line assuming x1 is on the x-axis and x2 is on the y-axis? 1 2 3 4 5% 0% 3% 92% 1. MRSx1,x2 2. MRTx1,x2 3. Ux1 4. All of the above

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10 Class 9 - Constrained Optimization (Mathematical) …the slope of my indifference curve is identical to the slope of my Budget Line… MRSx1,x2=MRTx1,x2
11 Class 9 - Constrained Optimization (Mathematical) MRSx1,x2=MRTx1,x2 To optimize, the rate at which I am willi ng to trade the goods… …must equal the rate at which the market dictates I trade them.

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Group-Clicker Question (P): Assume preferences are rational and monotonic. Assume at my current bundle, I would be willing to trade 1 unit of Good 1 for 2 units of Good 2. Assume the market prices are such that I could sell 1 unit of Good 1 for 3 units of Good 2. How could I end up better off? 1 2 3 73% 9% 18% 1. Sell Good 1 and buy Good 2. 2. Sell Good 2 and buy Good 1 3.
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9_MathematicalConstrainedOptimization_ToPost - .What...

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