Question

# 1. Suppose utility for a consumer over food(x) and clothing(y) is represented by u(x,y) = 915xy....

1. Suppose utility for a consumer over food(x) and clothing(y) is represented by u(x,y) = 915xy. Find the optimal values of x and y as a function of the prices px and py with an income level m. px and py are the prices of good x and y respectively.

2. Consider a utility function that represents preferences: u(x,y) = min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m.

3. Consider a utility function u(x1, x2) = ax1+bx2 and a budget line p1x1+p2x2=m If the absolute value of the slope of the indifference curve, a/b, is greater than the absolute value of the slope of the budget line, p1/p2 find the optimal consumption bundle.

4. Juliana's optimal consumption of movie tickets is given by the function x1=(3m)/(5p1), where m is her income and p1 is the price of a movie ticket. According to Juliana's preferences, movie tickets are inferior, neutral or normal good? Assuming her income (m=400.00) increases by \$100.00 and the price of a movie ticket is p1=2, by how many units does her consumption of movie tickets change?

5. Douglas consumes two goods, x and y. His utility function is u(x,y) = √� + � Let the price of good x be \$2 and the price of good y be \$2. Furthermore, assume that Douglas has \$420.00 to spend on these two goods. Find the demand for good x and y. Now suppose that the price of good x decreases to \$1.00. What is the income effect and substitution effect of this price change on the demand for x?

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