problem code : 090609MICRO

[vishruti]

A consumer has the following utility over childcare c and food f
U (c,f) = c^1/5 f^4/5

The price of childcare is pc = 2, the price of food is pf = 4 and income is I = 20

1. What is the consumer’s demand for childcare and food?

2. Suppose the government gives the consumer an income subsidy of S = 10. How
will the consumer allocate the subsidy in the consumption of goods c and f?

Suppose now the government decides to give an in-kind transfer to the consumer.
The in-kind transfer takes the form of 4 hours of childcare and 0.5 unit of food.
Assume that the transfer cannot be re-sold.

What are the new consumption levels after the in-kind transfer is given? What
is the level of utility attained by the consumer at this consumption level?

(source : MIT )

[namrata]

a.c =1 f =2
b c=3 f=6
the 3rd part am not very sure...if the gove gives the in kind subsidy,that is equivalent to 10 rs of the money income.but the consumer doesnt need to spend this 10 rs.so he has 20 rs and he consumes c =1+4=5 and f = 2.5
so his utilty is 2.87

[vishruti]

part a

c=2 and f=4

part b  c=3 f=6
 
third part

c=4 (because of the constriant) anf f = 5.5 ( from budget constraint)

[namrata]

can u xplain the 3rd part please

[vishruti]

when in kind subsidy is given then income increases to 30 because 4*2 + 0.5*4 = 10

and since it cannot be resold , we cannot consume at the optimum i .e . c = 3 and f = 6
becauce c>= 4 ( remember it cannot be resold) . hence c = 4 and substitute thin in 2c + 4 f = 30 this implies f = 5.5

hence c=4 f=5.5