这是美国的一个和计算经济相关的限时测试代写，要求使用Matlab

Directions: You have until midnight to finish the exam and upload your codes to the Canvas. Use
Matlab’s input command to allow me to choose the question number to execute your code as you did in
the homework questions.

1. Numerical Nonlinear Equation Solver: Write a Matlab code to solve the following nonlinear
equation for x 《 [1;5]:

2. Numerical Optimization: Write a Matlab code to solve the following monopolist firm’s profit
maximization problem using Matlab’s built-in functions fminbnd and fminunc for optimiza
tion:

where Q(p) = 10−2p0:8 and p 2 [0;10]: The output should display the profit maximizing price
and the associated profit. When coding use Matlab’s input command to allow me to choose
the method for the optimization.

3. On the Job Search Model: Consider a job search problem characterized by the following
Bellman equations:

where β = 0:996 is the discount factor, b = 0:4 is the unemployment benefit, δ = 0:02 is the job
separation probability, λu = 0:25 is the job finding probability for the unemployed, λe = 0:05
is the job finding probability for the employed. The wage distribution f is assumed to be
lognormal distribution with mean µ = −0:125 and standard deviation σ = 0:5. Write a Matlab
code that solves function W and scalar U. In your solution use Matlab’s built-in function
integral to solve for the integral terms and use Matlab’s built-in function interp1 with the
option spline to approximate the function W inside the integral. You can set the bounds for
the integral as 0 and 5 since F (0) = 0 and F (5) ≈ 1. Plot W (w) and U against w.