eco300 homework

Draw the graph of the indifference curve maps for each scenarios. Put good X on x-axis and good Y on Y-axis. Draw 3 indifference curves and labeled 𝑈1, 𝑈2, and 𝑈3, from the highest to the lowest utility level. ( You don’t need specific numbers here, refer to “four particular preferences” in the slides) a. Good X is economic bad. For good Y, more is better. b. Both of goods X and Y are economic bad. c. Good X is useless good and good Y is economic bad.

2. Draw the graph of an indifference curve map for the utility function 𝑈(𝑋,𝑌) = 𝑋2𝑌. Put good X on x-axis and good Y on Y-axis. Draw at least 3 indifference curves and label the utility level for each indifference curve. Explain why or why not do the indifference curves cross each other on the map.

3. Textbook page 77 Problem 2.3.

4. Textbook Page 77 problem 2.5.

5. 𝑈(𝑋,𝑌) = 𝑋0.7𝑌0.3, 𝑀𝑈𝑋 = 0.7𝑋−0.3𝑌0.3 𝑀𝑈𝑌 = 0.3𝑋0.7𝑌−0.7 𝑃𝑋 = 7 𝑃𝑌 = 6 𝐼 = 84 (a) Calculate and simplify the expression of the marginal rate of substitution 𝑀𝑅𝑆𝑋 𝑓𝑜𝑟 𝑌. Does this rate diminish as x increases and y decreases? (b) Write the budget constraint. (c) What is the consumption bundle to maximize the utility level? What is the maximum utility level?

6. Good X and good Y are complements. U(X, Y) = min (3X, 5Y). Price of X is $6 and price of Y is $5. The total income is $90. (a) Write the consumption ratio of good X and good Y. (b) Write the budget constraint. (c) What is the consumption bundle to maximize the utility level? What is the maximum utility level?

7. (a) Assume good X is normal. Plot a graph to illustrate the income and substitution effects of an increase in PX, holding PY and I constant. (b) Now suppose X is a Giffen good. Plot a graph to illustrate the income and substitution effects of an increase in PX, holding PY and I constant.

8. Textbook page 122 Problem 3.8.

9. Consider a linear demand curve, Q = 120 – 4P. a) What is the price elasticity of demand at P = 20? b) At what price is demand unit-elastic (i.e. elasticity = –1)?