Acknowledgement: While I was doing this assignment, there were a lot of difficulties, but I got support from some people to whom I am very much grateful.
First of all, I am grateful to my honorable course instructor, Professor Jamsheduzzaman, without motivations and guidelines of whom, it would not be possible for me to complete this type of Assignment. I also acknowledge the aid of his websites.
Secondly, I would like to thank the Author of the book ‘Managerial Economics-Peterson-4th edition’ which I have taken huge support.
Finally, I also like to thank some of my fellow classmates for working so hard and helping me to complete the assignment.
Abstract: This report is an attempt to establish the demand equation of a good Hamburger. I have estimated the Corresponding electricity. I have also compared Hamburger and Hotdog. The comparison exhibits:
- Was the Good a Substitute or Complimentary?
- Was the Good an Inferior or
- Was the good Basic Necessity?
I believe after studying my report one will be able to find the answer of the above queries.
Assumptions of demand are:
- Need utility
- Capacity to have it
- Willingness to spend capacity for it
There is an inverse relationship between prices and quantity demanded – as prices increases, quantity demanded will decrease.
The relationship between price and quantity creates two scenarios:
- Substitution Effect
- Income Effect
Demand Equation:
Qd = f (p)
Qd = a + bp
Where, p= price.
Multivariable:
Qd= f (P, I, Pz, T)
Where p= price, I= Income, Po = price of other goods and T= Consumer Preference.
Qd = a +b1P+ b2I + b3Pz + b4T
Here b1, b2, b3 and b4 indicate the change in quantity demanded of one unit changes in the associated variables i.e. the slope.
Elasticity: Elasticity is the percentage change in quantity demanded because of percentage change in any variable. Therefore elasticity is the slope of the demand equation.
Price Elasticity: Price Elasticity is the percentage change in quantity demanded because of percentage change in price.
%∆Q ∆Q/Q ∆QP
ξp = = = %∆P ∆P /P ∆PQ
Income Elasticity: Income Elasticity is the percentage change in quantity demanded because of percentage change in income.
%∆Q ∆Q/Q ∆QI
ξI = = = %∆I ∆I/I ∆IQ
Cross Elasticity: Cross Elasticity is the percentage change in quantity demanded because of percentage change in the price of another good (say z).
%∆Q ∆Q/Q ∆QPz
ξz = = = %∆Pz ∆Pz/Pz ∆PzQ
We know the demand equation is:
Qd = a +b1P+ b2I + b3Pz + b4T
In its present form this equation cannot be estimated using ordinary least squares because it is not linear. We assume a multiplicative equation. There is a simple transformation of the equation that allows it be estimated using least squares. First, we take logarithm of both sides of the equation and the result is:
Qd = a Pb1 Ib2 Pzb3 Tb4
Or, ln Qd = ln (a Pb1 Ib2 Pzb3 Tb4 ) eqn.ІOr, ln Qd = lna + lnPb1 + lnIb2 + lnPzb3 + lnTb4
Or, ln Qd = lna +b1lnP + b2lnI + b3lnPz + b4lnT eqn. ІІ The above equation is the multi variable equation. And the equation І can be estimated by the least square method. From the slope that is the coefficient of the equation ІІ we can calculate the elasticity. By calculus it was found that the coefficient of the variables of equation ІІ is the elasticity of that variable respectively. Hence,
b1 = ξP = Price Elasticity; b2 = ξI = Income Elasticity; b3 = ξZ = Cross Elasticity Determination of the Demand Equation: Here I have taken the consumption of hamburger (thousands of burger per week) in 10 different cities.
Table1: Hamburger Consumption
| City | Hamburger consumption, Qd | Hamburger price($) , P | Income($)(1,000s I | Hotdog price($) |
| A | 1 | 10 | 7 | 550 |
| B | 2 | 9 | 9 | 500 |
| C | 3 | 8 | 11 | 450 |
| D | 4 | 7 | 13 | 400 |
| E | 5 | 6 | 15 | 350 |
| F | 6 | 5 | 17 | 300 |
| G | 7 | 4 | 19 | 250 |
| H | 8 | 3 | 21 | 200 |
| I | 9 | 2 | 23 | 150 |
| J | 10 | 1 | 25 | 100 |
To calculate the regression line of the above variables I have taken the “ln” of the variables. The general form of the regression line is:
ln Qd = lna +b1lnP + b2lnI + b3lnPz |
Table2: Hamburger Consumption
| City | Hamburger consumption, lnQd | Hamburger price($) , lnP | Income($)(1,000s lnI | Hotdog price($), ln pz |
| A | 0 | 2.30259 | 1.94591 | 6.30992 |
| B | 0.69315 | 2.19722 | 2.19722 | 6.21461 |
| C | 1.09861 | 2.07944 | 2.3979 | 6.10925 |
| D | 1.38629 | 1.94591 | 2.56495 | 5.99146 |
| E | 1.60944 | 1.79176 | 2.70805 | 5.85793 |
| F | 1.79176 | 1.60944 | 2.83321 | 5.70378 |
| G | 1.94591 | 1.38629 | 2.94444 | 5.52146 |
| H | 2.07944 | 1.09861 | 3.04452 | 5.29832 |
| I | 2.19722 | 0.69315 | 3.13549 | 5.01064 |
| J | 2.30259 | 0 | 3.21888 | 4.60517 |
From computer program Excel the Regression Statistics was found such:
Table3: Regression Statistics
| Regression Statistics | | | |||
| | | ||||
| Multiple R | 0.998440571 | | | | |
| | 0.996883573 | | | | |
| Adjusted | 0.99532536 | | | | |
| Standard Error | 0.050117823 | | | | |
| Observations | 10 | | | | |
| | | | | | |
| | | | | | |
| | df | SS | MS | F | Significance F |
| Regression | 3 | 4.82084511 | 1.606948371 | 639.7607 | 6.61318E-08 |
| Residual | 6 | 0.01507078 | 0.002511796 | | |
| Total | 9 | 4.83591589 | | | |
| | | | | | |
| | Coefficients | Standard Error | t Stat | P-value | Lower 95% |
| Intercept | -17.90017623 | 4.19786035 | -4.26411903 | 0.005297 | -28.17197798 |
| X Variable 1 | -1.411509159 | 0.51701622 | -2.73010613 | 0.034181 | -2.676603205 |
| X Variable 2 | 2.633685824 | 0.18981131 | 13.87528376 | 8.73E-06 | 2.169233934 |
| X Variable 3 | 2.549188076 | 0.79646568 | 3.200625122 | 0.018585 | 0.60030533 |
Demand Equation:
From the Study of the Regression Statistics I found the Demand equation as follows:
Qd =17.90017623 -1.411509159P +2.633685824I + 2.549188076Pz
(-4.26411903) (-2.73010613) (13.87528376) (3.200625122)
R2 =0.99532536; DW = ; F =639.7607; Significance F = 6.61318E-08
Studying the t stat, R2, F and Significance F I have accepted the Regression equation of Demand.After accepting the Demand Equation I have found the elasticities as follows:
Price Elasticity Income Elasticity Cross Elasticity
ξP = -1.411509159 ξI =2.633685824 ξZ = 2.549188076
 |  | |
Table4: Elasticity
| Elasticity | Regression Line | Coefficient (Slope) | Result | Sign | Comment |
| Price Elasticity, ξP | Qd = 0.9701166 - 2.21018 P + 1.4343705I + 0.499868Pz | b1= - 1.411509159 | - 1.411509159 | Negative. | ξP >1 hence Elastic |
| Income Elasticity , ξI | b2 = 2.633685824 | 2.633685824 | Positive. | ξI >1 hence ; Elastic | |
| Cross Elasticity, ξZ | b3 = 2.549188076 | 2.549188076 | Positive. | ξZ >1 hence ; Elastic. |
Conclusion: After analyzing the results from Table4 I drew the following conclusions:
Price Elasticity was found Elastic and negative which indicates that the relationship between Hamburger consumption and Hamburger price is normal. With the increase of the price of Hamburger by $1 the consumption decreases by 1.411509159 Units. 
Income elasticity was found Elastic and positive. Therefore I can say it is normal and hamburger is superior goods. Because when Income increases by $1 the consumption of Hamburger also increases by 2.633685824 units.
Cross Elasticity was found Elastic and positive. Therefore I can say that with the increase of the price of another goods Hotdog by $1 the consumption of Hamburger increases by 2.549188076 units which indicates that Hamburger and Hotdog are substitute goods.
References:
v Managerial Economics- Peterson- 4th Edition
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