Gabby has the utility function U(X,Y) = X0.y0.26 When Gabby consumes X= 5 and Y=8 she has a marginal rate of substitution of X for Y equal to %3D
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- Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?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?Alice receives an allowance of 500 dollars that she spends on buying snacks (S) and tea (T). The price of each snack is 10 dollars and the price of each tea is 5 dollars. Her utility is given by: U (S, T) = 2S³/4 +T3/4 (a) Find her marginal rate of substitution (MRS) between S and T. (b) Write Alice's budget constraint. (c) Find Alice's optimal consumption and the optimal A. (d) What is her new consumption if the price of tea becomes 10 dollars? Note: numeric solutions for questions (c) and (d) are not integers.
- For the utility function U(X,Y)= 6X0.50.5, the marginal rate of substitution MRSxy is: O Y/X. O X/Y. 3Y/X. O3X/Y.Clara's utility function is U(x, y) =(x+2)(y+1). If her marginal rate of substitution is -4 and she is consuming 14 units of good x, how many units of good y must she be consuming?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 marginalrate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen toconsumer 12 units of X and 30 units of Y.
- Harry consumes 2 goods, X and Y and he spends N$60 per month. The price of good X is N$4 and the price of good Y is N$10. Harry's utility function is U(X, Y) = XY. (i) What is Harry's marginal rate of substitution? (5) (ii) What is the expression for Harry's budget constraint? (3) (iii) What is the slope of Harry's budget constraint? (2) (iv)Find the values of good X and Y maximizes Harry's utility. Show all your work. (6) (v) Illustrate Harry's utility maximizing combination on a clearly labelled graph. (4) (vi) Suppose the price of good X increased to N$6. Illustrate Harry's income and substitution effects on a well labelled graph. Show your work. (10) (vii) Suppose Genie is consuming two goods, coffee and beer. She spends all her income on a combination of coffee and beer where MUcoffee/Peoffee is 5 and MUbeer/Pbeer is 3. Explain why this combination is not maximizing her satisfaction. What should she do to maximize her utility? (5)Suppose Melina's utility for goods X and Y is represented by the following utility function: U(X,Y) = X1/4Y3/4. Find Melina's marginal rate of substitionA KU student maximizes his sporting utility by playing Golf (G) and Tennis (T). His function is given as: U(G,T) = G + T Graphically characterize the student’s indifference curve. What is the Marginal Rate of Substitution between Golf and Tennis What is the behaviour of the Marginal Rate of Substitution for these type of goods.
- Please solve all parts (d and e) Find the marginal rate of substitution of y for x [MRS(x,y)] for the following utility functionsDana's utility function is U(x,y) =3.2 x3.7y7.9. It follows if she has 2.4 units of good X and 1.1 units of good Y, her marginal rate of substitution (of good X in terms of good Y) is equal to ...