Scott consumes only butter (B) and honey (H). His utility function is U(B, H) = 4B + 5H,

where B is the quantity of butter and H is the quantity of honey. Suppose the price of butter is PB = 2, the price of honey is PH = 5, and Scott's income is M = 20 dollars.

(a) Draw Scott's indifference curves for U = 10 and U = 20, putting butter on the x-axis and honey on the y-axis. Clearly identify the intersections with each axis. (5 marks)

(b) In the diagram of part (a), draw Scott's budget line indicating the intercepts with the axes. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? Would Scott consume butter if the price of butter doubles (i.e., it increases to PB = 4)? Explain in detail. (5 marks)

(c) Obtain the Marginal Rate of Substitution (MRS) between butter and honey. Does the MRS satisfy the property of diminishing marginal rate of substitution? Are Scott's preferences strictly monotone? Are they strictly convex? Justify each of your answers. (5 marks)

(d) Scott's sister, Julie, has similar preferences to Scott's. For her, (BX , HX ) (BY , HY ) if and only if:

either 4BX +5HX > 4BY +5HY ,

or4BX +5HX =4BY +5HY andHX HY,

where BX and HX are the quantities of butter and honey, respectively, in the first bundle and BY and HY are the quantities of butter and honey, respectively, in the second bundle.

(d.1) Give an example of two bundles that reveal that the preferences of Scott and Julie are different. Explain how (and why) the preferences of Scott and Julie differ for these bundles. (2 marks)

(d.2) Are Julie's preferences complete? Justify your answer in detail. (3 marks)