Each month, Sophia spends her pocket money on toys (T) and icecreams (C). Her preferences an be represented by the utility function U(T, C)=8ln(T)+12ln(C). [Note: the derivative of In(x) 1/x.] a. [10 points] Compute the marginal rate of substitution of toys for icecreams. Is the MRS increasing or decreasing in toys? What does it mean? b. [10 points] Suppose that the price for toys is pr=20, the price of icecreams if pc=5, and Sophia's income is 100. What is the amount of toys and icecreams Sophia consumes if she maximizes utility subject to her budget? c. [10 points] Suppose that, because of a christmas related shortage, the price of toys increases to pr'=40. What is Sophia's new optimal bundle