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