This is similar problem with solutions compare to my problem. Look at the blue c

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This is similar problem with solutions compare to my problem. Look at the blue circle.

This is my problem that I should solve.

And this is my work.

My question is that I got two R values which are 5/4 and -4/3. Which R value should I use for finding M value?

Exercise 2 John has a weekly endowment of 140 dollars that he spends on buying games (G) and music cds (M). The price of each game is 30 dollars, the price of each cd is 20 dollars. John's utility is given y: a) Find John's Budget constraint b) Set up the Lagrangian and find his optimal consumption (assume both goods are infi- nitely divisible and express your answer in fractions if necessary) What is his new consumption if the price of games becomes 20 dollars? You may appeal to the MRS to avoid solving the Lagrangian c) Answer John's budget constraint: 140= 30G+20M Lagrangian: a) b) First order conditions: OM = 140-30G-2011 = 0 o2

Explanation / Answer

The variable R denotes the records, andit can't be negative, so that's why we will take only ositive value of R.

and thus, M=8(5/4)^2 = 8(25/16) = 25/2

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