1. Consider a utility function U (X A, X B) = XA X3. Let PA = $3 and PB = $2, and income is set at m = $40. Suppose PB falls to P3' =1. (30 pts.) a. Before the price change, what was X *A and X *3, the optimal consumption bundles? Sketch the original budget line and label the point (X *A and X *3) as A. Let XA be on the horizontal axis. (8 pts.) b. If, after the price change, income changed so that the original optimal bundle is just as affordable. What is the new income (m ')? At (PA, P'B, m '), what is the new optimal bundle (X 'A, X '3)? Sketch the budget line associated with (PA, P'B, m '). Label the point (X 'A, X '3) as B. (8 pts.) c. Does the substitution effect result in more X3? How many more of fewer? After the price change, how much XA and X3 are actually bought, (X \"A, X' '3)? Sketch the budget line associated with (PA, P's, m). Label the point (X ' 'A, \"3) as C. (5 pts.) (1. Along the vertical axis, label the income effect, the substitution effect, and the total effect on the demand for X3. The income effect of the fall in PB is the same as an (increase, decrease) in income of $_. (Choose \"increase\" or \"decrease\" and supply the missing value.) Does the income effect result in an increased consumption of X3? How much more? (5 pts.) e. Does the substitution effect of the fall in P3 make the consumer consume more or fewer XA? How much more of fewer? Does the income effect of the fall in the price of X3 make the consumer consume more or fewer of XA? What is the total effect of the change in the price of X3 on the demand for XA? (4 pts.)