Question

Picky Pete drags Indifferent Ian out for coffee at an upscale Italian cafe which sells only espresso (E) and biscotti (B). Picky Pete simply must have one biscotti for every espresso consumed, whereas Indifferent Ian views espresso and biscotti as perfect substitutes. One of their utility functions is given by U = min[E, B] and the other’s by U = E + B.

(a) Given the description, which utility function corresponds to which person?

(b) Suppose the prices of the goods are (pE, pB) = (2, 1) and Pete has allocated $12 for the outing while Ian brought only $4. Solve for each person’s utility-maximizing bundle of espresso and biscotti.

(c) Draw a fully labeled diagram illustrating Pete’s budget constraint, his optimal bundle, and an indifference curve representative of his utility at his optimal bundle. Indicate how much utility Pete obtains.

(d) Do the same for Ian

Answer 1

a).

Consider the given problem here “Picky Pete” must have one “B=biscotti” for every “E=espresso”, => “Pete” want to consume both the goods with equal proportion, => addition amount of “E” or “B” will not add any additional utility. So, here the utility function will be “L-shaped”, => it’s given by “U=min(E, B)”. Consider the following fig below.

Similarly, for “Lan” is indifferent between “1 unit of E” and “1 unit of B”, => “E” and “B” are perfect substitute, => “Lan’s” indifference curve is given by “U=E+B”. Consider the following fig.

b).

Now, “Pete” has “m=$12”, => the budget constraint is given by “2*E + 1*B = 12”. Now, “Pete’s” utility function is given by “U = min(E,B)”, => at the optimum “E = B”, => “2*E + B = 12”, => “2*E + E = 3*E = 12”, => E = 12/3 = 4, => E = B = 4. So, the optimum consumption bundles are given by “E=B=4”.

Now, “Len’s” utility function is “perfect substitute” type, => the utility function is given by “U = E + B”, => here “Len” will devote his entire income on the good which is cheaper. Here “Pb < Pe”, => “Len” will only purchase “B” and will not purchase “E”. So, the optimum consumption bundle are given by “E=0, B=4” given the available income.

c).

Consider the following fig.

B-Biscotti Pete's utility function and the budget line 2 E B12, U min(E, B) E1 В" 4 B1 E-Espresso

So, here “A1B1” be the budget line of “Pete”. Now, at the optimum “E=B”, => the optimum bundle is the intersection point between the budget line and the consumption ratio line. So, here “E1” be the equilibrium point of “Pete”.

d).

Consider the following fig.

So, here “A2B2” be the budget line of “Len”. Now here “E” and “B” are perfect substitute to each other and “B” is cheaper compare to “E”, => “Len” will purchase only “B” and not “E”. So, here “A2” be the equilibrium point of “Len”.