Define the Marginal Rate of Substitution between two goods (X and Y). If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginal rate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen to consumer 12 units of X and 30 units of Y.

Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2

QUESTION 1 Let qa be the quantity of apples and qo the quantity of oranges. A consumer's utility is described by the function u(qA.90)= 39A + 590 This consumer curently consumes 2 apples and 4 oranges. For this consumer, the marginal utilities are MUA= and MUO= Moreover, the marginal rate of substitution is MRSA O=

It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute 4 pounds of a generic store brand for 2 pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?