Economics
1. Suppose a consumer views two goods, X and Y, as perfect complements. Her utility function is given by U = MIN [2X, Y]. Sketch the graph of the consumers indifference curve that goes through the bundle X = 7 and Y = 8. Put the amount of Y on the vertical axis, and the amount of X on the horizontal axis. Which of the three assumptions that we made about consumer preferences is violated in this case?
2. Suppose a consumer has $250 to spend on two goods, Good X and Good Y. The price of Good X is given by PX = $10. The price of Good Y is given by PY = $25. Graph the consumer's budget constraint. Please put the quantity of Good X on the horizontal axis, and the quantity of Good Y on the vertical axis. Be sure to label your graph carefully and accurately. What is the slope of the budget constraint?
3. Suppose a consumer's preferences can be represented by the utility function U(X,Y) = XY2. In the table below, identify 4 points on the consumer's indifference curve where U = 100.
4. Suppose a consumer's preferences can be represented by the utility function U(X,Y) = Min (2X,Y). Also, suppose the consumer has $300 to spend and the price of Good X is PX = $2 and the price of Good Y is PY = $5. If the consumer maximizes their utility subject to their budget constraint, how much of Good X and how much of Good Y will the consumer purchase?
X* =
Y* =
5. Suppose a consumer's preferences can be represented by the utility function U(X,Y) = X*Y. Also, suppose the consumer has $320 to spend and the price of Good X is PX = $2 and the price of Good Y is PY = $4. If the consumer maximizes their utility subject to their budget constraint, how much of Good X and how much of Good Y will the consumer purchase?
X* =
Y* =