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ECON 202 Microeconomics Winter 2008 Economics Department Faculty of Management Technology Dr. Abdel-Hameed Nawar German University in Cairo Recitation Sheet 8 1. If the quantity of good ܽ (ܳ ) is plotted along the horizontal axis, the quantity of good b (ܳ ) is plotted along the vertical axis, the price of good ܽ is ܲ , the price of good ܾ is ܲ and the consumer's income is ܫ, then the slope of the consumer's budget constraint is: − − − − − ܳ /ܳ ܳ /ܳ ܲ /ܲ ܲ /ܲ ܫ/ܲ or ܫ/ܲ 2. Consider the following table which presents Mina's marginal utility for each good while exhausting his income. Bundle A B C D i. ii. iii. MUX 2.41 1.5 0.84 0.33 MUY Marginal Rate of Substitution (MRS) 0.25 0.31 0.42 0.66 Fill in the remaining column in the table. If the price of good X is twice the price of Y, at what consumption bundle in the table is Mina maximizing his level of satisfaction? Which market basket entails the largest level of good X consumption? Why? 3. Consider the following utility function: ܷሺܺ, ܻሻ = ܺ .ହ ܻ .ହ .. Holding the value of Y constant at 9, i. calculate and graph the marginal utility of X. Is it diminishing? ii. calculate and graph the total utility function. Is it diminishing? 4. Sophia consumes two goods, X and Y. The marginal utility of X and the marginal utility of Y satisfy the following equations: ܷܯ = ܻ ܷܯ = ܺ. The price of ܺ is EGP 9, and the price of ܻ is EGP 12. i. Write an expression for Sophia's MRS. ii. What is Sophia's optimal demand for X and Y? iii. Sophia is currently consuming 15 units of ܺ and 10 units of ܻ per time period. Is she consuming an optimal mix of X and Y? 5. Consider the following consumption expenditure data at three different price sets, and three consumption choices. For each pair of prices and demand choices: i. ii. iii. Draw the budget line and the point of choice. Apply the Weak Axiom of Revealed Preferences (WARP). Is there violation of consistent consumer behavior? Observation PX PY A 1 2 B 2 1 C 1 1 X 1 2 2 Y 2 1 2