Question

1. Tom likes cookies (c) and milk (ml). He always takes one cup of cookies with two cups of milk. Both cookies and milk cost $2 per cup. Tom has $24 to spend on these two goods. Consider a price drop in milk to $1 per cup.

   1. What kind of preferences does Tom have? Illustrate the shape of his indifference curves (cookies are measured on the y-axis).

   2. Derive his demand functions for cookies and milk.

   3. Find his optimal consumption bundle before and after the price change and write his budget constraint before and after the price change.

   4. Calculate the substitution effect and the income effect of the price change in Tom's demand of milk.

Answer 1

Solution

(a)

Let us consider Cookies as (c)and Milk as (ml).

Tom always takes one cup of cookies with 2 cups of milk.

Cost of Cookies: $2 and Cost of 2 Cups of Milk: $4

Total Income (M) = $24

Tom's preference is given by

f(c,ml) = min(c,2ml)

The above-given preference is called a perfect compliment preference as both goods are being consumed in a fixed quantity. It will have an L-Shaped indifference curve and the corner points are determined by c= 2ml

(b)

Tom's preference is given by

f(c,ml) = min(c,2ml)

Budget constraint is given by

p_cc + p_mlml = M (1)

Corner point is given by c = 2ml (Since L-shaped indifference curve) (2)

On solving (1) and (2) , we get;

p_c2ml + p_mlml = M

ml(2p_c + p_ml) = M

ml^* = M / (2p_c + p_ml)

c* = 2M / (2p_c + p_ml) [ Since c = 2ml]

(c)

We know that p_c = 2 ; p_ml = 4 and M = 24

ml* = 24 / (2*2 +4) = 24/8 = 3

c* = 2*24/((2*2 + 4) = 48/8 = 6

When the milk price drop by $1

Budget constraint is given by

p_cc + p_mlml = M

2c + 4ml = 24 ( Before price Change)

2c + 2ml = 24 ( after price Change)

Therefore ; p_c = 2 ; p_ml = 2 and M = 24

ml** = 24/(2*2 +2) = 24/6 = 4

c** = 2*24/ (2*2 + 2) = 48/6 = 8

(d)

When the goods are perfect complements, the substitution effect of a price change is zero. The income effect is equal to the total change.

Total Change = ml** - ml* = 4-3 = 1

Income effect = +1

Sustitution effect = 0