give explanation

1. Originally the consumer faces the budget line pixi + P272 = m. Then the price of good 1 doubles, the price of good 2 becomes 8 times larger, and income becomes 4 times larger. Write down an equation for the new budget line in terms of the original prices and income. 2. What happens to the budget line if the price of good 2 increases. but the price of good 1 and income remain constant? 3. If the price of good 1 doubles and the price of good 2 triples, does the budget line become flatter or steeper? 4. What is the definition of a numeraire good? 5. Suppose that the government puts a tax of 15 cents a gallon on gasoline and then later decides to put a subsidy on gasoline at a rate of 7 cents a gallon. What net tax is this combination equivalent to? 6. Suppose that a budget equation is given by pix, + Pzx2 = m. The government decides to impose a lump-sum tax of u, a quantity tax on good I of t, and a quantity subsidy on good 2 of s. What is the formula for the new budget line? 7. If the income of the consumer increases and one of the prices decreases at the same time, will the consumer necessarily be at least as well-off