Each day Paul, who is in third grade, eats lunch at school. He likes only twinkies (t) and soda (s), and these provide him a utility of

U(t, s) = √ ts,

where t is the quantity of twinkies and s is the quantity of soda.

(a) Calculate the MRS (marginal rate of substitution) of his utility function. Is the MRS a decreasing function of t?

(b) Suppose the price for twinkies is $1.0 each and soda costs $2.5 per cup. If each day, Paul can spend 10 dollars that his mother give to him, what is equation of his budget constraint?

(c) Since Paul's utility is increasing in quantity of both goods and MRS is diminishing, write out the necessary and sucient conditions for his utility maximization problem.

(d) Solve Paul's utility maximization problem by using the 2 equations in part (c), and provide the levels of Twinkies and Soda that maximize Paul's utility