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- If Porsha views 3 glasses of juice as a perfect substitute for one cup of soda and vice versa, what is her marginal rate of substitution between juice and soda?Compute marginal utilities and marginal rate of substitution for each of the utility functions given below. In cach case. explain whether the assumptions of diminishing marginal utility and diminishing marginal rate of substitution are satisfied or not. a) U(X,Y)= 2x-yi b) U(X,Y) = XY +3X + 5Y c) U(X,Y) = (0.3X + 0.7Y") d) U(X,Y) = In (5VX + 2VT) %3D %3D %3D2. What is the economic interpretation of the condition that the consumer at his optimum equates his marginal rate of substitution and the price ratio of the goods he consumes?
- b. i. Explain the concept of Marginal Rate of Substitution (MRS) as an important tool of indifference curve analysis of demandIn this particular example, what are the contributions of the income and substitution effects?Suppose a consumer has a monthly income of m = 100 which she spendson two commodities: french fries (x1) and beef jerky (x2). The price offrench fries is p1 = 2 and the price of beef jerky is p2 = 5.(a) Write down the consumer’s budget constraint (equation).(b) What is the maximal consumption of french fries (this is calledthe real income in french fries).(c) Find the maximal consumption of beef jerky (real income interms of beef jerky).
- A consumer's demand function for some good x is x=0,01m-2p, where m is income and P, is a good's price. Initially p,-20, 8000. Now assume that the price rises to p= 30 Calculate the income and substitution effects. Hint: you can use Slutsky approach, not Hicks.Given U(c, t)=3c+4t expalin what the utility function says about the marginal rate of substitution.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?
- 509 UNIT 1 ASSIGNMENT ECON 509 UNIT 2 ASSIGNMENT X PDF ars/Jo.. Tp AN Read aloud V Draw Highlight ECON 509 ASSIGNMENT UNIT ONE Answer All questions 1) a) Given the following typical utility curves determine whether they have convex indifference curves (that is, whether the Marginal Rate of Substitution declines as x increases). U(x. y)-x² -y? b) Given the following Constant Elasticity of Substitution production function, show whether or not it is homogeneous, and the scale it exhibits. Q = [L² + K']^ 2) Prove that the polynomial P(x) = -2x3 + 2x2 + 10x+ 6 has a zero at x 3, and factor the polynomial. %3D 3) The demand and supply functions for two related goods; jeans (x) and shirts(y). are given by15. Which of the following functional forms for utility suggests the greatest substitution effect when starting at the point where Px Py a. U-Xy12 b. U-X+Y c. U min (X, Y) d. U-XYMHarry 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)