Question

Physics-Step: "ou've probably already heard of economic "supply-demand curves" of price (P) "S. # of items produced. For example the "Demand" curve shows that as price coes up, demand goes down. The "Supply" (5) curve shows that as price goes up, companies want to produce more to sell. The "equilibrium price", at the ntersection of the two curves, is the price at which the market place will settle on Equilibrium assuming no other internal or external disruptions. price "our economics team has determined that the curves for the P-47D Thunderbolt model airplane kit (sold in hobby stores world-wide!) are: #produced (D): #produced - 30 + 24/P (S): #produced-p-19P+74 (where P = sales price, in dollars) herefore, to get the equilibrium price, you want to solve for Pin the equation: P.-19P+74 - 30+ * Price (P) O, you create the following function fIP), for which the root of flP) 0 is the desired equilibrium price : f(P)-P2-19P+44 For all the following problems, don't change this function! Just leave fIP) exactly as shown

-Create a "f(p)" MATLAB function (name it Price.m) so that it outputs the vlue of the function f(P)= P^2_19P+ 24/P
-Create a plot of f(P) over the range $0.00 to $20.00

-Finish code by writing own Secant Method to converge on the final solution for P:

%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%

% This script solves for the Equilibrium Price P, from the equation f(P)=0
%
% THIS IS JUST THE INITIAL CODE FRAGMENT. YOU NEED TO COMPLETE THE SCRIPT.
% *** ADD ADDITIONAL DOCUMENTATION! ***

%% INITIALIZATION OF VARIABLES FOR THE SECANT METHOD
clear

% Initial Bracket [P1, P2] and start the "P_history" vector of iterations
P1= 10; % DO NOT CHANGE P1 or P2 !!!
P2= 20; % " " " " " " !!!

P_history = [P1 P2]; % Will save each new Pk (k>2) as another element
% to the right in the vector P_history

% Tolerances (NEED TO REPLACE 0 PLACEHOLDERS)
tol_x = 0;
tol_f = 0;

%% PART [C]: ITERATIONS FOR THE SECANT METHOD

% Be sure to use a while loop, which continues iterating until BOTH
% convergence criteria ("proxy" AND "residual" error) are satisfied.

% You'll need to call Price(P) here somehow to get f(P) at each iteration,
% and use the last two iterations of P (and f(P)) to calculate the next
% iteration of price.
%
% Save the latest iteration of P in the vector of "P_history"

%% PART [D]: CONVERGENCE PLOTS OF "PROXY" and RESIDUAL ERRORS

% Calculate "proxy" error for all the (saved) Pk iterations in P_history
% Must start with "proxy" error for SECOND iteration (k=2), because
% you can't determine it for FIRST (k=1) iteration.

% Calculate residual error for all the (saved) Pk iterations in P_history
% Start with SECOND iteration (k=2), just to be consistent with "proxy"

% Plot the log10(proxy error) vs. iteration k -> save as Proxy_Plot.pdf

% Plot the log10(residual error) vs. k -> save as Resid_Plot.pdf

% Use built-in "fzero" to calculate MATLAB's solution to this problem, and
% calculate the "error" between fzero's answer and YOUR final, converged
% answer from [C].

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc
clear all
close all
format long
root = secant(@Price,1,3,1e-6,100);
fprintf('Root using secant is %.4f\n',root(end));
Proxy=abs(diff(root));
res=abs(Price(root));
fplot(@Price,[0,20]);
figure;
semilogy((2:length(root)),Proxy);
title('Plot of proxy error');
figure;
semilogy((1:length(root)),res);
title('Plot of res error');
p=fzero(@Price,5);
fprintf('The equilibrium price using fzero is %.4f\n',p);
function y=Price(p)
y=p.^2-19*p+44-24./p;
end
function root = secant(func, xrold, xr, es, maxit)
% secant(func, xrold, xr, es, maxit):
% uses secant method to find the root of a function
% input:
% func = function name
% xrold, xr = initial guess
% es = (optional) stopping criteria (%)
% maxit = (optional) maximum number of allowable iteraitons
% Outputs:
% root = real root
% if necessary, assign defualt values
if nargin<5, maxit = 50;end
if nargin<4, es = 0.001;end

% Secant Method
iter = 0;
while(1)
xrn(iter+1) = xr-((func(xr)/(func(xr)-func(xrold)))*(xr-xrold));% calculate the new xr
iter=iter+1; % next iteration
if xrn(iter)~=0 % xrn is not zero
ea = abs(xr-xrn(iter))/abs(xrn(iter)) *100; % Calculate the error
end
if ea<es | iter==maxit % Check the sopping criteria
break
end
xrold=xr; % set xrold equal to xr
xr=xrn(iter); % set xr equal to xrn
end
root = xrn;
end

- O X - OX Figure 3 File Edit Window HD H View Insert MATLAB R20 Figure 2 HOME File Edit View Insert Tools Desktop Window Help DOK SUA OE - O New Open Plot of proxy error 10° radeep Tools V Desktop Window Help A 3 DE Plot of res error O 100 Tax 10-2 ba Current Folder Name codegen convertFi example first 10-5 104 googlelin mathlab mynewdi 10-6 10-10 New folde questions simple_g! a1.m a2.m a3.m 10-8f a4.m 10-10 10-15 Details 1 2 3 4 5 7 8 1 2 3 4 5 6 7 8 10 12 Workspace New Name Value HP Proxy res root 1.7627 [0.3012,0.2848,0.1182... [2.5578,1.2432,0.8821,... [1.2857,1.5869,1.8718,... Root using secant is 1.7627 The equilibrium price using fzero is 1.7627 >> fx Price / secant Ln50 Col 4 ENG 10:13 AM - US 09/18/19 W Type here to search W

Kindly revert for any queries

Thanks.