Question 3: The inhabitants of an island are equally divided between two tribes:

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Question 3: The inhabitants of an island are equally divided between two tribes: the Quasi-Linears (QL) and the Cobb-Douglas (CD). The sole source of nourishment on the island is pineapples. Each tribe member lives for two periods. The endowment of a QL is 5 pineapples in each period, while the endowment of a CD is 10 pineapples in each period. The preferences of a QL tribe member are given by the utility function U (C1, C2) = 10 ln(C1) + C2, while the preferences of a CD tribe member are described  by the utility function (C1, C2) = C1C2, where C1is consumption of pineapples in period 1 and C2is consumption of pineapples in period 2. Despite their limited diet, the islanders are quite sophisticated. There is a central clearing house where each tribe can post offers of how many period 2 pineapples they will give up for a period 1 pineapple.

a. How are the posted offers related to the interest rate? What is the budget constraint of a member of the QL tribe? What is the budget constraint of a member of the CD tribe?

b. What is the gross demand for consumption by a QL tribe member for pineapples in Period 1? What is the gross demand for consumption by a QL tribe member for pineapples in Period 2? [Hint: The marginal utility of another period1 pineapple for a CD is C2and the marginal utility of another period 2 pineapple for a CD is C1. The marginal utility of another period1 pineapple for a QL is 10/C1and the marginal utility of another period 2 pineapple for a QL is 1.]

c. What are the net demands for consumption in period 1 for a member of the CD tribe? What are the net demands for consumption in period 1 for a member of the QL tribe?

d. What is the equilibrium interest rate or the price of period 1 pineapples in terms of period 2 pineapples? What tribe consists of lenders? How much do they lend? How much do they consume in period 2? Which tribe consists of borrowers and what is the period consumption of the borrowers?

Explanation / Answer

H.R.H. Prince Khalifa bin Salman bin Hamad Al Khalifa has served as the Prime Minister of the Kingdom of Bahrain since its independence in 1971. He is the second son of the former ruler of Bahrain Shaikh Salman bin Hamad Al Khalifa and the uncle of His Majesty King Hamad bin Isa bin Salman Al Khalifa.

H.R.H. was born on Sunday, 24th of November 1935 and grew up in the care of his father, H.H. Shaikh Salman bin Hamad Al Khalifa, ruler of Bahrain from 1942 to 1961. Ever since he was a child, his father instilled in him a strong sense of responsibility by assigning him to learn the Qur’an under the guidance of one of Bahrain’s most eminent scholars. Upon becoming 7 years of age, his father instructed that he and his brother attend his father’s court in which he met with Bahrain’s citizens to learn about their problems and concerns, and closely understand the manner by which his father ran the country’s affairs.

Before beginning his formal education in a government school, H.R.H. started his formal education and was assigned one of the most capable teachers of the time by his father. As a young man, he traveled intermittently to England to study from 1957 to 1959.

Mere hours after the signing of the document ending the special treaty between Bahrain and the United Kingdom on the 15th of August, 1971, H.M. Shaikh Isa bin Salman Al Khalifa, then Ruler of Bahrain, issued a decree to reorganize the political structure of the country.

As per the decree, the Emirate of Bahrain was renamed the State of Bahrain and the Ruler of Bahrain was changed to Emir of Bahrain. Another decree followed shortly thereafter which changed the State Council to Cabinet of Ministers and the President of the State Council to Prime Minister and Members of the State Council to Ministers.

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