Desperate David devours (consumes) only donuts and dumplings. Every donut costs $1.00 and every dumpling costs $1.50. His monthly budget for these items is $100. His mom makes dumplings at home at gives him 30 dumplings free every month. His dad owns a donut shop and gives him 50 free donuts every month.

a. Assuming David can not sell the gifts from his parents, draw his budget line and show the co-ordinates of all the important points on this budget line!!

b. Assuming that David is rational and possesses convex indifference curves, draw a diagram to show his optimum point if he spends half of his budget on donuts and half on dumplings. Show the co-ordinates of his optimum points and indicate how many donuts and dumplings he will consume every month. At the optimum point, the marginal utility of a donut is K times the marginal utility of a dumpling. The value of K is ________

c. Assuming that David is rational and possesses convex indifference curves, draw a diagram to show his optimum point if he consumes exactly 50 donuts a month. Show that if this is his optimum point, then marginal rate of substitution is not necessarily equal to the ratio of prices and he may be better off selling some of the donuts that his father gives him as a gift!

d. Draw his budget line if he is able to sell the gifts he receives from his parents. In this case what is maximum number of donuts that he can consume?