Need help with the 4 elasticities info below

Point Price Elasticity of Demand

Arc Price Elasticity of Demand

Income Elasticity of Demand

Cross-Price Elasticity of Demand

use information below for calculations

Demand equation

Q_D^X = A -B P_X + C P_Y + D M

where Q_D^X = quantity demanded of good X (corn)

P_X = market per unit price of good X (corn)

M = average consumer income

P_Y = price of the related good in consumption good Y (barley).

A = the intercept.

B,C,D = The estimated regression coefficients. Each regression coefficient represents the change in y relative to a one-unit change in the respective independent variable.

Based on the multiple liner regression analysis (Exhibit E) we can determine the equation as follows.

Q_D^X = 6.86 -0.63 P_X + 1.3 P_Y + .0006 M

Q_D^X is the predicted or expected value of the dependent variable .

Px, Py, M are the three independent or predictor variable,

The value of Q_D^X when all the independent variables are equal to zero is 6.86.

Interpretation of Parameter Estimates

Q_D^X = A -B P_X + C P_Y + D M

Q_D^X = 6.86 -0.63 P_X + 1.3 P_Y + .0006 M

Parameter estimate B: -0.63= change in QD/Change in P of corn

When holding all other variables affecting the demand of Corn constant, the relationship between QD of corn and P of corn is inversely related, thus the $1 increase in P corn will decrease the quantity demanded by -0.63.

Parameter estimate C : 1.3 = Change in QD of corn/Chanage in P barley

When holding all other variables affecting the demand of Corn constant, the relationship between QD corn and P barley is positively related, thus the $1 increase in P of corn will increase the quantity demanded by 1.3.

Parameter estimate D : 0.0006 = Change in QD of corn/Chanage in income

When holding all other variables affecting the demand of Corn constant, the relationship between QD corn and income is positively related, thus $1 increase in income will increase the quantity demanded by 0.0006.

Verify Significance

If the absolute value of the t-statistic is greater than 2, we conclude that the estimated coefficient is statistically significant at the .05 level.

Since t-stat of corn is -1.5the coefficient of price of corn -0.63 is less significant at 0.05 level.

Since the t-stat of Barley is 2.81which is > 2then the estimated coefficient of Barley = 1.3 is significant at the value of 0.05 level. Therefore we can be 95% confident that the price of barley has an impact on the quantity demanded of corn.

Since the t-stat of Income is 11 which is > 2then the estimated coefficient of Income = 0.0006 is significant at the value of 0.05 level. Therefore we can be 95% confident that income has an impact on the quantity demanded of corn.

Reduced demand equation

Q_D^X = 6.86 -0.63 P_X + 1.3 P_Y + .0006M

In this section we will be finding the reduced demand equation by holding price of barley and Income constant at year 2022

Q_D^X = 6.86 -0.63 P_X + 1.3 (7.3) + .0006(45,411)

= 6.86 -0.63Px + 9.49 + 27.25

= 43.6-0.63Px

Now let us plug the price of corn for year 2022

QDx = 43.6-0.63(6.6)

= 43.6 - 4.158

= 39.44 which is relatively close to the actual consumption of 36.

Disclaimer regarding Data:

The data collected for national income is per capita bases. The data found for consumption was per million per bushels and we had to divid it per population to find the per capital consumption. The corn consumption data found from USDA site is the total domestic use of corn but does not specify what type of use so we assume the total domestic use is the total national demand. We also used the yearly average data instead of monthly or quarterly. Even though we feel confident in the result of our analysis we strongly agree that with the use of first hand data and actual numbers a better result could be achieved.

Graph of Demand Curve:

In order for us to draw a graph we have to find the value of QD of corn when Price of corn is zero and we have to find the Price of corn when QD of corn is zero. This can be easily done by using the reduced equation.

QDx =43.6-0.63Px

when Px = 0 QDX = 43.6

When QDx = 0 Px = 69.2

Exhibit D
Year	Corn Consumption in million	population in million	Corn Consumption per capita	Price of Corn	Price of Barley	Average Personal Income
1975	4103	215.97	19	2.54	2.42	19910
1976	4144	218.04	19	2.15	2.25	20347
1977	4311	220.24	20	2.02	1.78	20778
1978	4882	222.58	22	2.25	1.92	21498
1979	5203	225.06	23	2.52	2.27	21676
1980	4891	227.22	22	3.11	2.79	21580
1981	4978	229.47	22	2.5	2.48	21887
1982	5428	231.66	23	2.55	2.18	22157
1983	4806	233.79	21	3.21	2.47	22714
1984	5182	235.82	22	2.63	2.29	24061
1985	5267	237.92	22	2.23	1.98	24566
1986	5893	240.13	25	1.5	1.61	25269
1987	6041	242.29	25	1.94	1.81	25597
1988	5232	244.5	21	2.54	2.8	26558
1989	5753	246.82	23	2.36	2.42	27080
1990	6034	249.62	24	2.28	2.14	27304
1991	6331	252.98	25	2.37	2.1	27137
1992	6808	256.51	27	2.07	2.04	27896
1993	6293	259.92	24	2.5	1.99	27991
1994	7175	263.13	27	2.26	2.03	28410
1995	6321	266.28	24	3.24	2.89	29011
1996	6991	269.39	26	2.71	2.74	29585
1997	7287	272.65	27	2.43	2.38	30303
1998	7314	275.85	27	1.94	1.98	31712
1999	7578	279.04	27	1.82	2.13	32410
2000	7799	282.16	28	1.85	2.11	33644
2001	7911	284.97	28	1.97	2.22	34216
2002	7903	287.63	27	2.32	2.72	34894
2003	8330	290.11	29	2.42	2.83	35473
2004	8842	292.81	30	2.06	2.48	36324
2005	9134	295.52	31	2	2.53	36525
2006	9081	298.38	30	3.04	2.85	37570
2007	10300	301.23	34	4.2	4.02	38094
2008	10159	304.09	33	4.06	5.37	38189
2009	11062	306.77	36	3.55	4.66	37815
2010	11202	309.32	36	5.18	3.86	38282
2011	10943	311.56	35	6.22	5.35	38769
2012	10353	313.83	33	6.89	6.43	39731
2013	11535	315.99	37	4.46	6.06	38947
2014	11883	318.3	37	3.7	5.3	40117
2015	11765	320.64	37	3.61	5.52	41383
2016	12353	322.94	38	3.36	4.96	41822
2017	12361	324.99	38	3.36	4.47	42669
2018	12220	326.69	37	3.61	4.62	43826
2019	12185	328.24	37	3.56	4.69	45105
2020	12074	331.5	36	4.53	4.75	47729
2021	12484	331.89	38	6	5.31	48534
2022	11955	332.84	36	6.6	7.3	45411