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# Write all import statements here

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize

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# Define model parameters here

params = np.array([100,1.03,1.02,0.95])

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 def U(sol,params):
    """
    Returns the lifetime utility of a young person as a function of his consumption and money holdings (sol)
    
    as well as the parameters of the model (params)
    
    """
    y, z, n, beta = params

    return - (sol[0] ** (1/2) + beta * sol[1] ** (1/2) + (beta ** 2) * sol[2] ** (1/2))
    # Write your code here

    
def V(params):
    """
    Returns the solution to the optimization problem as a function of the parameters of the model
    
    """
    y, z, n, beta = params
    cons = ({'type': 'eq', 'fun': lambda sol: sol[0] + sol[3] - y},
           {'type': 'ineq', 'fun': lambda sol: sol[1] - (n/z) * sol},
           {'type': 'eq', 'fun': lambda sol: sol[2] - ((n ** 2)/(z ** 2)) * sol[3] + (n/z) * sol[1]})
    bnd = [(0,np.inf),(0,np.inf),(0,np.inf),(0,np.inf)]
    lös = minimize(lambda sol, params: -U(sol,params), x0=[25,25,25,25], method='SLSQP', args=params, constraints=cons, bounds=bnd, options={'disp': True,'ftol': 1e-10})
    return lös
    # Write your code here
    

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z_grid = np.linspace(1.0,3.0,100)
q_star = np.zeros(len(z_grid))
c_1 = np.zeros(len(z_grid))
c_2 = np.zeros(len(z_grid))
c_3 = np.zeros(len(z_grid))
u = np.zeros(len(z_grid))

for i, z in enumerate(z_grid):
    params[1] = z
    q_star[i] = V(params).x
    c_1[i] = params[0] - q_star[i]
    c_2[i] = q_star[i] * params[2] / params[1]
    c_3[i] = ((params[2] ** 2) / (params[1] ** 2)) * q_star[i] - (params[2] / params[1]) * ((V(params).x[1] * q_star[i]))
    u[i] = U(q_star,params)

c = c_1 + c_2 + c_3
Iteration limit exceeded    (Exit mode 9)
            Current function value: 14.262500001558012
            Iterations: 101
            Function evaluations: 1262
            Gradient evaluations: 98
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
TypeError: only size-1 arrays can be converted to Python scalars

The above exception was the direct cause of the following exception:

ValueError                                Traceback (most recent call last)
<ipython-input-196-1e981037e672> in <module>
      8 for i, z in enumerate(z_grid):
      9     params[1] = z
---> 10     q_star[i] = V(params).x
     11     c_1[i] = params[0] - q_star[i]
     12     c_2[i] = q_star[i] * params[2] / params[1]

ValueError: setting an array element with a sequence.

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 plt.figure(figsize=(9,6))
plt.plot(z_grid,c_1,label=r'$c_1$')
plt.plot(z_grid,c_2,label=r'$c_2$')
plt.plot(z_grid,c_3,label=r'$c_3$')
plt.ylabel(r'Real consumption, c',fontsize='12')
plt.xlabel(r'Money growth rate, $z$',fontsize='12')
plt.legend(loc='best',fontsize='12')
plt.show()