Question

Rick always likes to consume a cup of tea with a serving of noodles at any given time of the day. He earns a monthly allowance of 150. A cup of tea cost him Rs5 and serving of noodles cost Rs 10. Given this what will be Rick’s optimal consumption bundle?

Answer 1

$I = 150\\ P_t = 5\\ P_n =10$

Here, t is denoted as Tea and n is denoted as noodles.

Therefore,

$I=(P_t)t+(P_n)n\\150=5t+10n ........... (i)\\Now,\\Slope \space of\space IC = −MRS_{t,n}=−\frac{MU_t}{MU_n}\\ MU_t=n\\ MU_n=t\\Slope\space of\space IC=−\frac{t}{n}\\Slope\space of\space Budget\space line=−\frac{Pt}{Pn}\\ =−\frac{5}{10}\\ =−\frac{1}{2}$

Slope of IC = Slope of Budget Line

$−\frac{t}{n}=−\frac{1}{2}\\\frac{t}{n}=\frac{1}{2}\\2t=n ........... (ii)$

Now by putting the value of n in equation (i) we get,

$150=5t+10(2t)\\ 150=5t+20t\\ 25t=150\\ t=6\\ Or \space t^*=6$

Now, putting the value of t in equation (ii) we get,

$2(6)=n\\ n=12\\ Or \space n^*=12$

Hence Rick’s optimal consumption bundle is t* = 6 and n* = 12