Question 1 (20 marks).Scott consumes only butter (B) and honey (H). His utility function is

U(B, H) = 4B+ 5H,

whereBis the quantity of butter andHis the quantity of honey. Suppose the price of butter is

PB= 2, the price of honey isPH= 5, and Scott's income isM= 20dollars.

(a) Draw Scott's indifffference curves forU= 10andU= 20, putting butter on thex-axis and

honey on they-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 toPB= 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:

either4BX+ 5HX>4BY+ 5HY,

or4BX+ 5HX= 4BY+ 5HYandHXHY,

whereBXandHXare the quantities of butter and honey, respectively, in the fifirst bundle

andBYandHYare 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

difffferent. Explain how (and why) the preferences of Scott and Julie diffffer for these

bundles. (2 marks)

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