Ambrose consumes only nuts and berries. Fortunately, he likes both goods. The consump- tion bundle where Ambrose consumesx1units of nuts per week andx2units of berries per week is written as (x1; x2):The set of consumption bundles (x1; x2) such that Ambrose is indi erent between (x1;x2) and (1;16) is the set of bundles such thatx10; x20 andx2= 204px1:The set of bundles such that (x1; x2) is indi erent to (36;0) is the set such thatx10; x20 andx2= 244px1:

(a) Plot several points that lie on the indi erence curve that passes through the point (1,16) and sketch this curve using blue ink. Do the same, using red, for the indi erence curve passing through the point (36,0).

(b) Use pencil to shade in the set of commodity bundles that Ambrose weakly prefers to the bundle (1,16). Use red ink to shade in the set of all commodity bundles (x1;x2) such that Ambrose weakly prefers (36,0) to these bundles. Is the set of bundles that Ambrose prefers to (1,16) a convex set?

(c) What is the slope of Ambrose's indi erence curve at the point (9,8)?

(d) What is the slope of his indi erence curve at (4,12)?

(e) What about the slopes at the points (9,12) and (4,16)?

(f) Do the indi erence curves you have drawn exhibit diminishing marginal rate of substi-

tution?

(g) Does Ambrose have convex preferences?