Regression Essay

Developing a linear regression model and estimate the effects of a tariff

a)      To describe the data using diagrams and any statistics that seems appropriate.

The price mean and the standard deviation is 2.0461 and 0.4337 respectively, quantity mean and standard deviation is 495.2852 and 22.7671 respectively. The table below shows the results:

Price:

price

Mean
2.046062012
Standard Error
0.111975629
Median
1.95338747
Standard Deviation
0.433679748
Sample Variance
0.188078123
Quantity:

quantity

Mean
495.2852178
Standard Error
5.878442947
Median
500.8603165
Standard Deviation
22.76711164
Sample Variance
518.3413722

b)      To check if there is a trend in prices or the quantities demanded over the years?

c)      (i) To compute 95% confidence intervals for prices and quantity demanded.  Having the price mean and the standard deviation as 2.0461 and 0.4337, 95% confidence interval can be computed as;

            Lower Interval = (-1.96*0.4337) + 2.0461 = 1.196

            Upper interval = (1.96*0.4337) + 2.0461 = 2.8962

Thus 95% confidence interval for price is (1.196, 2.8962).

Having the quantity mean and standard deviation as 495.2852 and 22.7671, therefore 95% confidence interval can be computed as;

            Lower interval = (-1.96*22.7671) + 495.2852 = 450.6265

            Upper interval = (1.96*22.7671) + 495.2852 = 539.9087

Thus 95% confidence interval for quantity is (450.6265, 539.9087).

(ii) Confidence intervals show the interval in which the value of price or quantity can fall at, while simple mean just show a single value for the expected value of price or quantity.

(d) Using linear regression, the inverse demand for Bananas can be estimated as;

P = f’ (Q)       and Q = 594.96 – 48.522P

 Thus inverse demand function is P = 10.76601 – 0.01761Q.

(e) The regression equation and the adjusted R-squared.

       Q = 594.96 – 48.522P and adjusted R-squared is 0.8431.

(f) Is demand for the year 2009 elastic or inelastic?  What did you expect for agricultural products?

Using the formula  , where ?Q = -3.717, ?P = -0.222, P =1.448, and Q = 522.478. Thus ed = (-3.717/-0.222)*(1.448/522.478) = 16.7432 / 0.00277 = 6044.4765

(g) Graph of demand function and supply function:

From the chart the equilibrium price and quantity is approximately 2.845217594 and 456.9043519 respectively.

 (h) To estimate the change in Producers’ and Consumers’ surplus from the imposition of the tariff that resulted in prices increasing from 1.448 to 1.7 euros per kilogram.

Supply = P=-20+0.05Q

Price = 1.448

1.448 =-20+0.05Q

Q = 428.96

Price = 1.7

1.7 =-20+0.05Q

Q = 434

Demand = Q = 594.96 – 48.522P

Price = 1.448

Q = 594.96 – 48.522(1.448)

Q = 524.7001

Price = 1.7

Q = 512.4726

Table summarizes the results:

price
supply
demand
1.448
428.96
524.7001
1.7
434
512.4726
The diagram below indicates the equilibrium and the changes in supply and demand due to the tarrif:

Consumer surplus change = (price change X quantity change)/2

Producer surplus change = (price change X quantity change)/ 2

Consumer surplus = area A

Area A = [2.845 X (594.96 – 456.90)] / 2

Area A = 196.3992

Producer surplus = area B

Area B = [2.845 X (456.90-400)] / 2

Area B = 80.95

The following table summarizes the results;

price
supply
demand

1.448
428.96
524.7001

1.7
434
512.4726
equilibrium
2.845217594
456.9044
456.904352
at price zero
0
400
594.96
equilibrium consumer surplus
196.399

equilibrium producer surplus
80.95

change
0.252
5.04
-12.2275
producer surplus change

1.27008

consumer surplus change

3.08133

From the table producer surplus declines by 1.27008 whereas consumer surplus declines by 3.08133