Question

Charlotte consumes only flies, f, and gnats, g. As she has long lost the ability to spin web, she relies on the local market, Zuckerman’s general store. The price of flies is pf , and the price of gnats is pg. Charlotte’s income is Y .

(a) Write and graph Charlotte’s budget constraint, denoting all key intercepts and slopes.

(b) The price of gnats at Zuckerman’s general store increases to p'g . Write and graph Charlotte’s budget constraint, denoting all key intercepts and slopes.

(c) Return to part (a). Zuckerman’s introduces an exciting new pricing strategy. The first u units of flies and the first u units of gnats are free. After that, standard pricing (pf or pg) prevails. Draw Charlotte’s new budget constraint.

(d) In the same graph as part (c), draw the budget constraint if Charlotte’s income rises to Y' > Y . Similarly, draw the budget constraint for incomes Y'' and Y''', where Y''' > Y'' > Y' > Y (all on the same graph).

(e) For fun, connect the kink points on the graph from part (d).

Answer 1

Given price of flies= pf

Price of gnats = pg

Income = Y

Let F denotes the quantity of flies and G as quantity of gnats.

a) Charlotte's budget constraints

Y = pf * F + pg * G

pg * G = Y - pf *F

G = (Y - pf *F)/ pg

Gnats on y-axis and Flies on x-axis.

y and x intercept respectively are thus,

if F = 0, g = Y/pg

and if G = 0, F = Y/pf

slope = -pf/pg

Gnats T/PE Flies

b) Price of gnats has increased to p'g

the new budget constraint is

p'g * G + pf * F = Y

y-intercept if F= 0, G = Y/p'g

x-intercept if G = , F = Y/pf

new and decreased slope is -pf/p'g

tilt in budget constraint bесами а increased price of gnats - TIPG flies

c) since first u units of both the goods are free. the budget constraint will have a kink at (u,u) units of F and G.

The new budget constraint is -

pg (G-u) + pf (F-u) = Y

first free l'unite caused a kinkin - the budget - constraint

d) The increase in income causes budget constraints to shift parallely.