Question-3 (Finding optimal bundle)utility functions and budget constraints.1. U(₁, ₂) = 3x₁ +2x2 and 6x₁ + 2x₂ = 242. U (1, 2) = ₁ + 2x2 and 3x1 + 6x2 = 483. U (11, 12) = min{1, 2} and 41 + 2x2 = 481. U(T1, T₂) = min{4x1, 2r2} and 2x₁ + 3x2 = 36Find the optimal bundle using the following

An optimal bundle is the combination of two goods that provide a consumer with the highest utility…

Question-3 (Finding optimal bundle) utility functions and budget constraints. 1. U (₁, ₂) = 3x₁ +2r2 and 6x₁ + 2x2 = 24 2. U(1, 2) = ₁ + 2x2 and 3x1 + 6x2 = 48 3. U (11, 12) = min{1, 2} and 4x₁ + 2x2 = 48 1. U(1,₂)= min{4x1,2x2} and 2x₁ + 3x2 = 36 Find the optimal bundle using the following

Question-3 (Finding optimal bundle) utility functions and budget constraints. 1. U (₁, ₂) = 3x₁ +2r2 and 6x₁ + 2x2 = 24 2. U(1, 2) = ₁ + 2x2 and 3x1 + 6x2 = 48 3. U (11, 12) = min{1, 2} and 4x₁ + 2x2 = 48 1. U(1,₂)= min{4x1,2x2} and 2x₁ + 3x2 = 36 Find the optimal bundle using the following

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4 Part Question on Caesar * * PART 1 * * Caesar has preferences that are described by the utility function u = 3x 1 + 5x 2. Caesar strictly prefers the bundle (x 1, x 2) = (0, 6.6) to the bundle A. (3, 3) B. (5, 3.6) C. (0, 8.4) D. (11, 1.8) E. (8, 3.60) * * PART 2 * * What is the functional form of Caesar’s preferences, or indifference curves? A. Linear (perfect substitutes) B. Leontief (perfect complements) C. Satiation D. Concave, but not strictly concave E. Cobb-Douglas * * PART 3 * * Caesar’s preferences are A. strictly convex. B. definitely not well-behaved. C. definitely well-behaved. D. strictly concave. E. neutral. * * PART 4 * * Caesar has been consuming the bundle (x 1, x 2) = (10, 2.4). At this point, what is the marginal rate of substitution? A. – 0.25 B. –0.6 C. – 1.67 D. – 3.0 E. – 5.0.
(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? < (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain.< (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility (U*). Show your work. < (g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to (e)? Explain in simple terms and show in a diagram.<
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Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices på and på for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. = (c) Suppose a = . Suppose also that John has income I = 1 and pv 2. What is the value of John's optimal happens if John's income doubles to I = 400? 200 and faces prices p consumption bundle? What =
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If the utility function (U) between food (F) and clothing (C) can be represented as U = F*C, then which combination of food and clothing will a rational consumer choose? a. (F, C) = (9, 25) O b. (F, C) = (25, 4) O c. (F, C) = (4, 16) d. (F, C) = (4, 25)
Find the optimal bundle using the following utility functions and budget constraints. 1. U(x,y)=lnx+yand2x+y=10 2. U(x,y)=3x+2yand3x+2y=24 3. U(a,z)=3a+2zand3a+6z=24 4. U(a,z)=a2z2 and4a+2z=485. U(x,z)=a2z3 and3a+2z=36