Question

Assume Miss Muffet eats curds, whey, and strawberries. Her utility function is given by U(c, w, s) = c · w · s, where each letter stands for quantities of the different foods. Suppose that the ratio of the price of curds to that of whey ( pc /pw ) never changes.

(a) How might one define a composite commodity for dairy product, say, d?

(b) What are Miss Muffet's demand functions for d and s?

(c) Once Miss Muffet decides how much to spend on d, how will she allocate those expenditures between c and w (i.e., what fraction of her expenditures on d will go to c and w, respectively)?

Answer 1

ANS - In real life , a consumer normally consume more than one goods . In such a situation, 'Law of Equi-Marginal Utility' helps in optimum allocation of his income . It is also called 'Law Of Satisfaction OR GOSSEN'S Second Law .

In this , Miss Muffet eats curds , whey , strawberries by taking these three goods . In case of one commudity the consumer spent entire income on one commodity . Now we discuss equilibrium of consumer by taking these three goods or his satisfaction level .

Given , Utility function is - U(c,w,s) =c X w X s

According to the law of Equilibrium marginal utility , a consumer gets maximum satisfaction , when ratios of MU of three commodities and there respective prices are equal and MU falls as consumption increases . It means , there are two necessary condition's to attain Consumer's Equilibrium in case of three commodities .  

(1) Marginal Utility MU of last rupee spent on each commodity is same

A consumer is consumption of single commodity C is equilibrium = MUc/Pc=MUm

similarly a consumer consuming another commodity W will be equilibrium MUw/Pw=MUm

According to this we get MUc/Pc =MUw/Pw=MUm

In this , the marginal utility of money or price is assumed to be constant . So , the equilibrium condition can be

MUc/Pc = MUw/Pw OR MUc/MUw = Pc/Pw

So , Miss Muffet in consumption of these commodities will be at equilibrium when she spents her limited income in such a way that the ratios of marginal utilites of two commodities and their price are equal and MU falls as consumption increase .

Let explain with the help of example ,

The law of equi Marginal Utility with the help of a numerical example ;

Suppose total money income of the consumer is rupees 5 which she wishes to spend on two commodities c and w . Both these commodities priced at Rs 1 per unit . So consumer can demand maximum 5 units of c and 5 units of w . In thius we show the marginal utility which the consumer derives from various units of c & w .

Units MU of commodity c MU of commodity w

( in units ) ( in units )

1 20 16

2 14 12

3 12 8

4 7 5

5 5 3

According to this table , Miss Muffet will spend the first rupee on commodity c which will provide her utility of 20 utils . The second rupee will be spend on commodity w to get utility of 16 utils . So the Miss Muffet demand the combination of both two goods when :

1 MU of last rupee spend on each commodity is same

2 MU falls as consumption increases

It happens when Miss Muffet buy three units of c and two units of w .