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# Lab1 - Statistics 103 Lab 1 LAB PROBLEMS Find the total...

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Statistics 103: Lab 1 LAB PROBLEMS 1. Suppose that the tax t i paid by individual i is the following function of his or her income x i : t i = 0 . 1( x i - 2000) (i.e. , there is a flat tax of 10% on all income over \$2000). You know that total income in a geograph- ical area containing 500 individuals is \$5 , 000 , 000. What will the total tax revenue be? answer: 400,000 2. In a particular geographical area, the demand func- tion for each person i for a particular good is q d i = 100 + . 2 x i - 9 p where q d i is quantity demanded for person i , x i is person i ’s income and p is the commodity’s price. For firms in this area the supply function for this good is q s j = - 50 + 20 p where q s j is the quantity supplied of the good by firm j . There are 5 firms and 100 consumers. Total income of the consumers is \$100 , 000. Equilibrium occurs where 100 X i =1 q d i = 5 X i =1 q s j (i.e. , market demand equals market supply). Find the equilibrium price. answer: \$ 30.25 3. Suppose x 1 = 2, x 2 = - 1 and x 3 = 0. Compute 3 i =1 5 x i + 2 and 3 i =1 1 x i +2 answer: 11; 1.75 4. Suppose ¯ x = 11 and define y

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Lab1 - Statistics 103 Lab 1 LAB PROBLEMS Find the total...

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