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It would be good to publish tomorrow.
Please help with the editing, I've reset as best I can, also attached a file as it should be.
Please help edit, I've reset as best I can, also attached a file as it should be.
Nothing showed up on the orbit. Something has been done wrong. Do it again.
Nothing has appeared in orbit. Something has been done wrong. Do it again.
Maybe I could attach the files here and you could compile the articles?
No, no, it's not our job to put it together, the administration will do it. You upload it, we'll take a look.
You need to attach as a zip file, just the Office document will not attach.
You can dump it now: it's Friday and it's April 1st.
here we go
No, no, it's not our job to put it together, the administration will do that. You upload it, we'll take a look.
You need to attach in zip format, just the Office document will not attach.
It's Friday, it's April 1st.
All right, I'll spend my night time, make people a present by the deadline. /granit77/
Please see if it goes like this?
MINISTRY OF EDUCATION OF THE REPUBLIC OF TAJIKISTAN
INSTITUTE OF ECONOMICS AND TRADE
TAJIK STATE UNIVERSITY COMMERCE
DEPARTMENT OF ECONOMICS AND ENTREPRENEURSHIP
SCIENTIFIC REPORT
on the topic: "Dependence of profit of commercial structures
on the dependence of profit of commercial structures on the selling price of goods
Compiled by: associate professor of the department
"Economics and Entrepreneurship",
D. in Technical Sciences Sultonov Yu.
Khujand, 2010
Profit dependence of commercial structures on selling price
Profit (P) is defined as the difference between income (E) and costs, which can include acquisition or production costs (Pt), variable costs, which depend on income (Pd), fixed costs (Pn) and wages and salaries (Zr) :
P = Y - Rt - Rd - Rn -1.25* Zr ; (1)
Under market conditions, the amount of good sold (K) depends on its selling price (Ts) and this relationship can be represented as a hyperbola equation /1/:
K = a + c/C ; (2)
By multiplying both parts of equation (2) by CD, we obtain income as a straight line equation
D = Dm + a*C ; (3)
Here:
Dm is the maximum income generated at Ts close to the cost price or the wholesale purchase price of the product Tspok;
a is the proportionality factor, which is numerically equal to a change in revenue when the selling price of Ц changes by one;
Coefficients Дм and а can be determined by the actual values of income Дi, obtained at the corresponding values of Цi price, by the method of least squares:
Dm = ( ∑ Di * ∑ Tsi^2 - ∑ Tsi * ∑ Tsi* Di ) / ( n* ∑ Tsi^2 - ( ∑ Tsi ) ^2 ) (4)
а = ( n* ∑ Цi* Дi - ∑ Цi* ∑Дi ) / ( n* ∑ Цi^2 - ( ∑ Цi ) ^2 ) (5)
n is the amount of data;
Pt can be expressed in D as follows:
Rt = CP/C*D; (6)
The variable costs depending on income (Pd) can be defined as follows
Рd = k*D ; (7)
where: k is a generalized proportionality coefficient summing up the effect of all variable costs depending on income
Now the profit equation (1) after transformation can be represented as
P = a*(1- k)*(C^2 - A*C + B)/C; (8)
Where:
A = Ts0 + Tsk + Tsr; (9)
B = Ts0*Tsk-Tsr; (10) Ts0 = -Dm/a - the price limit when income D = 0; (11)
Cp = Cpk/(1-k); (12)
price = (Ppp+1,25*Zr)/(a*(1-k)); (13)
Ppp is the entrepreneur's fixed cost of sales.
Applying condition P = 0 to equation (8), we define the sale price for two breakeven points Ts1 and Ts2
TS1 = A/2 - ((A/2)^2 - C)^0.5; (14)
TS2 = A/2 + ((A/2)^2 - C)^0.5; (15)
Now the profit equation (8) can also be represented in the following form:
P = -a*(1-k)*(C2-C)*(C-C1)/C; (16)
Equating the first derivative from (8) on Ц, we get a ratio for determination of optimal price value, which provides maximal profit Pmax :
Tsopt = B^0.5; (17)
Pmax = a*(1-k)*(Tsopt^2 - A*Tsopt+B)/Tsopt; (18)
Pmax = -a*(1-k)*(Ts2-Tsopt)*(Tsopt-Ts1)/Tsopt; (19)
Equation (8) can be converted to the form:
Pmax = -a*(1-k)*((Ts2-Tsopt)-(Tsopt-Ts1)); (20)
From equality (19) and (20) follows the following relation which we believe is true for any market:
Tsopt*((Ts2-Tsopt)-(Tsopt-Ts1)) / (Ts2-Tsopt)*(Tsopt-Ts1)=1 ; (21)
It is useful to note the following relations derived from the properties of the parabola contained in (8):
A=C1+C2 (22)
B=C1*C2 (23)
Now from (17) we can derive the relationship between the values of Ts1, Ts2, and Tsopt also in the form :
Tsopt=(Ц1*Ц2)^0.5; (24)
Consequently, by studying the pattern of change in profits through the method we have proposed, it is possible to optimize the activities of commercial structures depending on the price of goods sold in the market environment.
As an example, let us consider the optimization of the trading process of a commercial structure operating under the simplified system of taxation.
It was known that when the price of the goods purchased at the level of 3.45 somoni, the daily income was 21534 somoni, and when it was increased to 3.75 somoni it fell to 8130 somoni per day. Selling Expenses (Pp) constitute 3 percent of revenue and Entrepreneur's fixed costs (Ppp) are at the level of 30 somoni per day. Employees' wages (ZR) are set at 50 somoni per day.
We need to determine the optimal value of the selling price of the goods to ensure maximum profit.
For this let us define coefficients Dm and A of income equation (3) by relations (3) and (4):
Дм = ((21534+8130)*(3,45^2+3,75^2)-(3,45+3,75)*(3,45*21534+3,75*8130))/
(2*(3,45^2+3,75^2)-(3,45+3,75)^2) = 175680
а = (2*(3,45*21534+3,75*8130)-(3,45+3,75)*(21534+8130))/
(2*(3,45^2+3,75^2)-(3,45+.3,75)^2) = -44680
Now determine the coefficients of the profit equation (8):
k = kn +cr
kn = krp+xp+kdp - generalised coefficient of tax deduction from income under the simplified taxation scheme, retail sales tax (Crp), social tax (SST) and tax on entrepreneur's income (TI), respectively
NRp = krp*D = 0.03*D (25)
Nsn = ksn* DD = 0.002* DD (26)
Ndp = kdp* DD = 0.04*(Y-Nrp) = 0.04*(1-0.03)* DD = 0.0388* DD (27)
kn = 0.03+0.002+0.0388 = 0.0708 (28)
RR = Cr*D = 0.03*D (29)
k = 0,0708+0,03 = 0,1008
Consequently, the variable cost, according to (7), will be
Pd = k*D = 0.1008*D
Cp = -Dm/a = -175680/-44680 = 3.9320
K = Kpk/(1-k) = 3/(1-0,1008) = 3.3363
Cr = (Ppp+1,25*Zr)/(a*(1-K)) = -(30+1,25*50)/(-44680*(1-0,1008) = -0,0023
A = C0+Ck+Cp = 3.9320+3.3363-0.0023 = 7.2660
Q = C0*Cp-Qp = 3.9320*3.3363+0.0023 = 13.1182
Let us define 2 break-even points by (14) and (15):
TS1 = A/2 - ((A/2)^2 - C)^0.5 = 7.2660/2 - ((7.2660/2)^2-13.1182)^0.5 = 3.3495
Q2 = A/2 + ((A/2)^2 - C)^0.5 = 7.2660/2 + ((7.2660/2)^2-13.1182)^0.5 = 3.9164
The profit equation (8) takes the form:
P = a*(1-k)*( C^2-A*C+B)/C=
= -44680*(1-0,1008)*(Ц^2-7,2660*Ц+13,1182)/Ц;
Fig. 1. shows a graph of the relationship between profit and market price,
calculated for this commercial structure according to this equation.
Let's define the value of optimum price (Tsopt), which provides maximal profit Pmax according to (17)-(20):
Tsopt = B^0.5 = 13.1182^0.5 = 3.6219
Pmax = a*(1-k)*(Tsopt^2 - A*Tsopt+B)/Tsopt =
= - 44680*(1-0.1008)*(3,6219^2-7,2660*3,6219+13,1182)//3,6219= 889.7993
Pmax = -a*(1-k)*(Ts2-Tsopt)*(Tsopt-Ts1)/Tsopt =
= (1-0.1008)*44680*(3,9164-3,6219)*(3,6219-3,3495)/3,3495= 889.7993
Pmax = -a*(1-k)*((Ts2-tsopt)-(Tsopt-ts1)) =
= 44680*(1-0.1008)*((3,9164-3,6219)-(3,6219-3,3495)) = 889.7993
Let us now determine Pmax using the traditional formula (2):
Dopt = Dm + a*Copt = 175680-44680*3.6219 = 13853.2837
Рt = Doppl * Dopk / Doppl = 13853,508*3/3,6219 = 11474,5833
Рd = k*Dopt = 0.1008*13853.508 = 1396.4110
Pmax = Dopt - Pt - Rd - Rn - 1,25*Zr =
= 13853,2837 - 11474,5833- 1396,4110 - 30- 1,25*50 = 889,7993
It should be noted that the calculated and actual values of Pmax coincide completely.
Further, let us confirm the validity of our proposed relations (14) and (15) for determining the break-even points C1 and C2 also by the traditional formula (2):
D1 = Dm + a*C1 = 175680 - 44680*3.3495 = 26022.5560
D2 = Dm + a*C2 = 175680 - 44680*3.9164= 694.4769
Pt1 = Dm*C/C1 = 175680/(1 + 3,3495) = 23306.9824
Pt1 = Dm*C/C2 = 175680/(1 + 3.9164) = 531.9736
Rd1 = k*D1 = 0.1008*26022.5560 = 2623.0736
Rd1 = k*D1 = 0,1008*694.4769 = 70.0033
P1 = D1 - Pt1 - Rd1 - Rp - 1.25*Zr = 26022.5560 - 23306.9824 - 2623.0736 -
- 30 - 1.25*50 = 0.0000
P2 = D2 - Pt2 - Rd2 - Rp - 1.25*Zr = 694.4769 - 531.9736 - 70.0033
- 30 - 1.25*50 = 0.0000
Literature:
1.Christopher Dougherty, Introduction to Econometrics, Moscow, INFRA-M, 1998.
I have these posts on my profile about articles ready to be published, where did they go?
7.2660/2 - ((7,2660/2)^2-13,1182)^0.5 = 3,3495
Yusuf, of course I am not a censor, but I want to ask: what kind of style of scientific report is it when an example of practical application of this or that obtained expression is given in detail down to algebraic operations with numbers. In your report this mathematics occupies 90% of the whole volume... What for? Do you want to impress everyone with your numeracy? Why to keep so many significant digits after decimal point in received figures if the final result is presented without indicating a confidence interval?
P.S. Give me a link to your dissertation work. Better yet, post it here.