1. Consumer's utility is U=5x1+7x2. Price of good 1 is fixed at 10, income isI. Derive the demand function for good 2.
2. Consumer's utility is min(2x1,x2). Utility is U, prices are p1and p2. What is the bundle that minimizes this consumer's expenditure?
3. A consumer purchases two goods: x1and x2. The Engel curve for x1is a straight line from the origin with slope 6, the Engel curve for x2is a straight line from the origin with slope 12. The price of good 1 is 4. What is the price of good 2?
4. Take a consumer whose income is 32 and the utility function isx1+2(square root of x2). The price of good 2 is fixed at 4. The price of good 1 decreases from 8 to 4. What are the income and substitution effects of this price change?
5. Consumer's utility is3(square root of x1)+2(square root of x2). Derive the Hicksian demand for good 2 corresponding to utility level U.