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Please solve all 3 parts

4. An individual's preferences over books (B) and snacks (S) are represented by the utility function, $U(B,S)=[B_{I/2}+S_{I/2}]_{2}$. According to the MRS, what's the maximum number of books the individual would be willing to give up for one more snack, if the individual currently has 16 snacks and 4 books? a. 4 b. $1/4$ c. 2 d. $1/2$ 5. An individual has preferences represented by the utility function: $U(x,y)=x(2y?5)$. Which of the following statements is TRUE concerning her marginal rate of substitution of $x$ for $y$ ? a. If the individual has 10 units of $x$ and 10 units of $y$, she would be willing to trade a maximum of $4/3$ units of $y$ to get 1 additional unit of $x$. b. If the individual has 3 units of $x$ and 4 units of $y$, she would be willing to trade a maximum of 2 units of $x$ to get 1 additional unit of $y$. c. If the individual has 2 units of $x$ and 4 units of $y$, she would be willing to trade a maximum of 4 units of $y$ to get 3 additional units of $x$. d. If the individual has 10 units of $x$ and 5 units of $y$, she would be willing to trade a maximum of 4 units of $y$ to get 1 additional unit of $x$. e. All the statements above are false. 6. Kassia's preferences are monotonic in both $X$ and $Y$. Moreover, she is willing to give up increasing amounts of good $Y$ for each additional unit of good X. Which of the following utility functions could represent Kassia's preferences? a. $U(X,Y)=X_{2}+Y$ b. $U(X,Y)=(X_{1/2}+Y_{1/2})_{2}$ c. $U(X,Y)=XY+X$ d. $U(X,Y)=(X_{2/3}Y_{1/3}+4)_{2}$

4. Answer is option (d) i.e