Show the utility maximizing choice of X and Y for a consumer whose preference set is strictly convex. Assume the consumer exhausts his/her income on...

6. Show the utility maximizing choice of X and Y for a consumer whose preference set is strictly convex. Assume the consumer exhausts his/her income on the purchase of both goods. Be sure to label all the axis, lines, curves and points. Explain what the graph is saying (in complete sentences and paragraphs).

7. Assume that a consumer accidently picks a combination of X and Y such that the relative price of PX to PY (PX/PY) is less than the marginal rate of substitution of X for Y (MRSX,Y). What does this mean? What would the consumer do under these conditions, would he/she buy more X and less Y, or would it be the other way around? Why? Explain both verbally (using complete sentences) and graphically (being sure to properly label all the axis and curves and what they mean).

8. Draw a diagram (in two dimensional space with X on the horizontal axis and Y on the vertical axis) showing the income and substitution effects in the consumption of good X as a result of a decrease in its price. Assume that good X is a normal good. Be sure to properly label all the axis and curves. Below the diagram write paragraph that explains what's happening in the graph.

9. Draw a diagram showing how an individual's offer of labor will change as a result of an increase in the wage rate, assuming that the individual can easily substitute consumption for leisure; there are no necessities. Be sure to label all the axis and curves. Below the diagram write paragraph (or more) explaining the graph and what is meant by the income and substitution effect. Assume that the income effect is equal to the substitution effect.

10. Draw a diagram showing how an individual's offer of saving will change as a result of an increase in the interest rate. Assume that the individual can easily substitute future consumption for current consumption and that the income effect outweighs the substitution effect. Be sure to label all the axis and curves. Below the diagram write paragraph (or more) explaining the graph and what the income and substitution effects mean.