In this problem a firm's production function depends only on labor, L: outputequals (L – aL?). The firm pays a fixed wage, w, per unit of employed laborand incurs hiring costs equal to qH?, where H is the amount of new hires,and receives a constant price, p, per unit of output. The firm's labor force hasa constant quit rate equal to 8. Solve for the path of hiring that solvesTe-"[p(L – aL²) – wL – qH²]dtmaxsubject toL = H – SLL(0) = LoThis is an optimal control theory problem from thebook Mathematics for Economics by Micheal Hoy.Please solve this in the right way.

In this problem a firm's production function depends only on labor, L: outp equals (L – aL²). The firm pays a fixed wage, w, per unit of employed lab and incurs hiring costs equal to qH?, where H is the amount of new hire and receives a constant price, p, per unit of output. The firm's labor force h a constant quit rate equal to 8. Solve for the path of hiring that solves e-"[p(L – aL?) – wL – qH?]dt max | 0,

In this problem a firm's production function depends only on labor, L: outp equals (L – aL²). The firm pays a fixed wage, w, per unit of employed lab and incurs hiring costs equal to qH?, where H is the amount of new hire and receives a constant price, p, per unit of output. The firm's labor force h a constant quit rate equal to 8. Solve for the path of hiring that solves e-"[p(L – aL?) – wL – qH?]dt max | 0,

Survey Of Economics

10th Edition

ISBN:9781337111522

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter10: Labor Markets And Income Distribution

Section: Chapter Questions

Problem 3SQP

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Derive the labor hiring rule for a profit maximizer firm in the short-run and give a graphical example to explain your argument with a graphically