UMP_Notes - 1) MRS > P x /P y , then X = I/P x...

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Utility Maximization Problem 1. Cobb-Douglas or other nicely behaved utility functions - example: U = X 1/2 Y 1/2 - “interior” solution => x>0 and y>0 - solve the following two equations for X and Y MRS = P x /P y P x X + P y Y = I 2. Leontief Utility function(“L”shaped utility function) - example : U = min[aX, bY] - “interior solution” - find “Helping” equation and use budget constraint aX = bY P x X + P y Y = I 3. Linear Utility Function - example: U = aX + bY - Consider “Corner solution”
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Unformatted text preview: 1) MRS > P x /P y , then X = I/P x and Y = 0 2) MRS = P x /P y , then X is anything between 0 and I/ P x and remaining income will be spent on Y 3) MRS < P x /P y , then X = 0 and Y = I/P y- Use Graph 4. Quasi-linear Utility Function- example: U = V(X) + Y- Interior + Corner- Suppose interior. Use MRS = ERS and Budget constraint Find Price range where Y>0- Then, you can find the price range where Y 0. In this range, Y = 0 and X = I/ P x...
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