## Equation 1 above may be linearized using the following transformations:

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**Part A**

You have been commissioned to write a report for *Royal Dutch Shell PLC* relating to the demand ofpetroleum in different countries. Details regarding the format for the report are presented on page 3.

**Model 1 Price elasticity demand estimation:**

Downloadthe price and quantity (petroleum consumption) data from Blackboard.

The demand function takes the general form:

**….(1)**

where e< 0 and *A* is a constant

**Note: Equation 1 above may be linearized using the following transformations:**

** **

**….(2)**

- In the first of these, a = ln
*A* (where *A* is defined in equation 1). To obtain the antilog of a, take *e* to the power of a. The slope b = the power e in equation 1.

**Model 2 Multivariate demand estimation**

** **

A new team of analysts has been employed by *Royal Dutch Shell PLC*, and they report that, having obtained more data, the demand for petroleum, is best represented by a multivariate demand equation:

**….(3)**

All variables are expressed in logarithms.

where *Q*_{x}is the quantity demanded of product *X*; *P*_{x}, is the price of X; *P*_{y} is the price of product *Y;M* is income and *ε* is a random error term.

Using the data given below, and using the EXCEL DATA-ANALYSIS tool (or a similar package such as SPSS, SAS, Eviews, Minitab, STATA, R,or MATLAB), estimate the demand equation given above.

**Sample:**

**Petroleum consumption**: US (EIA2005); UK (EIA1959); Canada (EIA1961); France (EIA1956); Germany (EIA1957); Italy (EIA1958); Japan (EIA1962); South Korea (EIA1963).

**Petroleum Price: **Crude Oil-Brent Spot FOB (EIACRBR).

**Coal & Gas Price**: International Coal & Gas Price Index (USIPE059F).

**Income**: US GDP (USGDP...D); UK GDP (UKGDP...D); Canada GDP (CNGDP...D); France GDP (FRGDP...D); Germany GDP (BDGDP...D); Italy GDP (ITGDP...D); Japan GDP (JPGDP...D); South Korea GDP (KOGDP...D).

**Time period**: Q1 2000 – Q2 2017

**INSTRUCTIONS FOR PRESENTATION OF DATA :**

Model (1) Ordinary Least Squares (OLS) Bi-variate Linear Regression

and

Model (2) Ordinary Least Squares (OLS) Multivariate Linear Regression

Your report should take the general form:

**Part I: Introduction**

A brief introductory statement.

**Part II: Estimating constant-price elasticity of demand function**

- The demand function for petroleum should be estimated in different countries, with clear presentation of tables used in the calculation of the important values, plus graphs of
*ln(Q)* versus *ln(P)*, and comment on their trends. You should also graph and comment on the change of petroleum consumption and price during 2000-2017.
- Explain the importance of the OLS model slope estimate in relation to the own-price elasticity, and calculate/explainhow responsive consumers are to a 1% increase in the price of the product.Which country’s petroleum consumption is more likely to be affected by the price? Are your results all in accordance with the law of demand? Explain.
- Comment on the diagnostics: ‘t’ statistic, p-value, R
^{2}, adjusted-R^{2}, and the ‘F’ test.
- The owner of a small chain of petrol stations in Newcastle read an article in a trade publication stating that the own price elasticity of demand for petrol in the UK is -0.07. Because of this highly inelastic demand in the UK, he is thinking about raising prices to increase revenues and profits. Do you recommend this strategy based on the information he has obtained? Explain.
- Suppose
*OPEC* announce to decrease the supply of crude oil next year, in the meantime, *The Wall Street Journal* predict that the demand of crude oil will also reduce due to the recent economy recession. What effect will this have on price?

**Part III: Estimating multivariate demand function **

- Transform the original dataset to
*ln* dataset, anddraw graphs of*ln(Py)*and *ln(M)*, comment on their change during 2000-2017 compared to the change of *ln(Q)* and *ln(Px).*
- The multivariate model should be estimated, with a clear presentation of results of tables used in the calculation of the important values, comment on the significance of the variables and validity of the regression.
- Explain the size and sign (ie. + or -) of each coefficient and whether this accords with your expectations and economic knowledge.If not, what reasons may bias your results? Comment on your answer.
- On the basis of the results, which independent variable(s) should be most concerned with – and does this make sense given the product being analysed? Explain your answer.

**Part IV: Discussion**

- Comment on any possible problems with this model or methodology.
- What other data may have been useful when assessing demand for petroleumand why?
- Comparing model 2 with model 3, which do you think is more plausible? Explain your answer.
- Additional issues of relevance.

**Part V: Conclusion**

A brief concluding statement.

#### References/Bibliography/Appendix

(Total words DO NOT include any words in this part.)

**Part B**

The book store in Newcastle recently advertised that “**buy one, get one free–limit one free book per customer**”. You stepped into the store and asked a clerk, “Will you sell me one book for half price?” The clerk answered, "I can`t do that."When you started to leave the store, the clerk hastily offered, "However, I am authorized to give you a 40 percent discount on any book in the store." Assuming you have £100 to spend on books (X) or all other goods (Y), and that books cost £50 per book, answer the following questions:

a. Illustrate the consumer`s opportunity set with the "buy one, get one free" deal and with a 50 percent discount, and explain your answer.

b. Why was the 40 percent discount offered only after the consumer rejected the "buy one, get one free" deal and started to leave the store?

c. Why was the clerk willing to offer a "buy one, get one free" deal, but unwilling to sell a book for half price?

d. The management of this book store is considering a plan to terminate a new employee. The action stemmed from documented evidence supplied by the store`s accounting department that this new employee did not add as much to the store`s overall output as did a worker hired two weeks earlier. Based on this evidence, do you agree that the latest worker hired should be fired? Explain.

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