Reference no: EM131139524
1. Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = x1.9 x2.1. If their income is $100, and the prices of goods one and two are $10 each, what fraction of the consumer's income will be spent on good one?
2. Suppose that a consumer has preferences for goods one and two represented by the utility function u(x1, x2) = x1 + x2. Suppose that the consumer's income is $100 and the price of good two is $10. Plot the consumer's demand curve for good one with the price of good one on the y-axis. Please label at least three points on the graph, and be as clear as possible. Show all your work.
3. Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = x1.6 x2.4. Suppose that the price of good one, p1, increases. Use calculus to show what will happen to demand for goods one and two, x1* and x2*. Are the goods substitutes, complements or neither? Show all your work.
4. Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = ln(x1) + ln(x2). Suppose that the consumer's income, m, suddenly increases. Use calculus to show what will happen to demand for goods one and two, x1* and x2*. For each good determine whether it is an inferior or normal good. Show all your work.
5. Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = min {5x1, 10x2}. Suppose that the price of good one, p1, increases. Use calculus to show what will happen to demand for goods one and two, x1* and x2*. Are the goods substitutes, complements or neither? Show all your work.
6. Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = min {3x1, 2x2}. Suppose that the consumers income, m, suddenly decreases. Use calculus to show what will happen to demand for goods one and two, x1* and x2*. For each good, determine whether it is an inferior or normal good. Show all your work.
7. Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = x12/3x21/3. Suppose that the originally the price of good one is $3, the price of good two is $3 and the consumer's income is $99. Furthermore, suppose the price of good one then decreases to $1. Calculate the substitution effect and the income effect on good one.
8. Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = min {2x1, x2}. Suppose that the originally the price of good one is $2, the price of good two is $2 and the consumer's income is $12. Furthermore, suppose the price of good one then increases to $4. Calculate the substitution effect and the income effect of the price increase on good one.
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