For each of the following utility functions answer the following questions (i-iv): i) Calculate the marginal utilities MUx and MUy ii) Calculate MRSx,y and determine if this is diminishing as good x increases iii) if I=80, Px= 4, Py=2, determine the utility maximizing basket. iv) Determine the demand curves for good x and y   (a). u(x,y)= 6x^2/3 +2y (b) u(x,y)= 3x+7y

Hello, I am not understanding this practice problem. I dont know how to solve the second half .

2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where x represents the number of cans of soda and y represents the number of juice boxes. a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y). b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda and juice. Write Ping's demand curve for juice (y). Illustrate his demand curve. c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and $30, resp.). Use your demand functions to find his best bundle. In an indifference curve diagram illustrate his best bundle at these prices. For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the prices of the two goods are unchanged at Px= $1.5 and Py= $1. d) Use your demand functions to find his new best bundle. e)…

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