In FanWangEcon/PrjOptiAlloc: The Optimal Allocation of Resources Among Heterogeneous Individuals

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Outline

In this file, we solve a linear spline inversion problem that is required for solving the inequality constrained planner optimization problem given CRS CES or linear one input production function.

1. G1: Provide parameters and draw four linear lines, where 1 line's y-intercept is positive, 2 lines' y-intercepts are negative, 1 line's y-intercept is 0. All lines are linear. One of the line with negative y-intercept has the same slope as the origin line. Slopes are all monotonically increasing. Draw random parameters in fact. Allow for more than 4 lines, many many lines possibly.
2. G2: Find, Mark out on graph the x-intercepts.
3. G3: Draw the unconstrained sum of the lines
4. G4: Draw the constrained sum of the lines, where by constraint we mean only the parts of the lines where y(x)>0
   • figure could be presented as summed area plot
5. G5: Solve for and identify the y values corresponding to x-intercept for the linear summed spline
6. G6: Invert the figure

Function parameter features

• So there are 6 figures, this should be written as a function so that arbitrarily more positive and negative sloped lines could be added. Should also be possible to have identical lines.

FanWangEcon/PrjOptiAlloc documentation built on Jan. 25, 2022, 6:55 a.m.