1/2 1/2 Frank's preferences over q₁ and q₂ are given by U (91, 92) = 91 92 and he has an income of Y = 128. The price initial prices are p₁ = 4 and p2 = 16. Suppose that the price of g₁ increases to 13. What are the compensating variation (CV) and the equivalent variation (EV) in absolute value? |CV = 120.56 and |EV = 48 |CV = 102.76 and |EV = 57 |CV=88.76 and |EV = 81 |CV = 19.33 and |EV = 24 |CV = 134.67 and |EV = 123 000
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- A consumer has a perfect complements utility function, where she prefers to have one unit of H with each unit of G. Also, she has an income of $210. Assume that the price of H is $8 and the price of G is $6. What is the consumer's optimal choice for good G*? Group of answer choices 11 12 15 16Bob has a utility function U(x, y) = √x1 + 0.8√x2 + 0.64√x3 over his incomes x1, x2, x3 in the next three years. This function is an example of (A) expected utility; (B) quasi-hyperbolic utility function; (C) discounted utility; (D) none of the above. . Which of the following preferences agree with Bob’s utility? (A) (9, 10, 11) ≻ (9, 10, 12); (B) (9, 10, 11) ≻ (11, 10, 9);(C) (9, 10, 11) ≻ (9, 11, 10); (D) none of the above. Bob’s utility function implies (A) time stationarity; (B) transitivity; (C) impatience; (D) all of the above.Given the Utility Function is U = X0.7Y0.3 and Budget is taka 300. The original price was (Px, Py) = (2, 2) and the new price is (Px’, Py) = (4, 2). (a) Draw an angle curve for X by using the above information [Labelling is must] (b) Calculate the value of Compensation variation (CV) and Equivalent variation (EV)?
- Steve's utility for socks (q1) and other goods (q2) is given by U(q1,q2) = 10q10.1 0.1q² 0.9 The price of the composite good is p2=1 and the price of a pair of socks is p1=2. Steve's income is Y=100. Every year, Steve's mom buys him 20 pairs of socks. How many dollars is the equivalent variation of the $40 that his mom spends on socks every year?Utility functions of a consumer: U = 20x10.4x20.4 Specify:a. marginal utility of each item.b. If the consumption of x1seee is 80 and x2 as much as 60 units, the price of Px120 and Px2 25, Determine if there is a balance of consumption?1. What is the relationship between pS/pC and pC /pB? What feature of the utility function is responsible for these ratios?2. Now suppose that the moment before the above prices are elicited, the subject gets $10, which does not become part of her reference point. Again calculate the three prices pS, pB, and pC. What is the relationship between pS/pC and pC /pB? Why? 3. In some actual experiments, subjects were not given money, and pS/PC was found to be about 2, and PC/pB was found to be about 1. Write down a utility function that can produce these ratios.
- Q12. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F.Suppose as Case X, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $15, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space.The utility function of a certain consumer is U =(x1,x2)= x11/3 x22/3 , x 1and x 2 is the consumption of two kinds of goods, and the consumer's income is 100. The current prices of the two kinds of goods are P 1 =1 and P 2=2 respectively, ask: 1. If the price of the first commodity increases from 1 to 2, and other factors remain unchanged, what is the total effect of the price increase on the consumption of the first commodity? According to the Slutsky decomposition principle, what are the income effect and substitution effect? 2. Calculate the amount of income compensation that changes the price of the first commodity from 1 to 2, keeping the original effect unchangedSolve; a consumer utility function is given as 64q10.5q20.25q30.4 1. what is the marginal utility of consuming commodities q1, q2 and q3 2. derive the second-order partial derivatives of the utility function with respect to the three pairs of commodities 3. show the cross partial derivatives with respect to q1 4.what is her total utility when q1 is 24, q2 is 30, and q3 is 15
- Q4. Explain with the aid of well labelled diagram(s) whether this statement is True, False or Uncertain, given the information provided below:“Two goods, A and B are perfect substitutes with prices $PA and $PB respectively. The income of an individual is given by $Y. Initially, $PA = $PB.It is claimed that in a particular situation where $I is assumed to remain unchanged and if due to some exogenous factor, $PB < $PA, the budget line will pivot, become flatter and optimal bundle will be a corner solution (0,B*) and no other possibility would exist.Assume a consumer has a well-behaved utility function (e.g. strictly increasing, diminishing MRS) with an income of $80. Suppose the price of good X is $2 and the price of good Y is $8. Assuming the consumer has chosen the optimal market basket, what is the consumers marginal rate of substitution at that consumption level? Group of answer choices 4 not enough information 40 10 .25Q 2. Xinyi has an income of I = 140, and faces prices px = 1 and py = 2. Her utility function is U(x,y) = xy + x. (a) (a) Find her optimal consumption bundle, using the Lagrangian. (Note: You are not required to do so here, but it would be good practice to also solve for Xinyi's demand function for x by leaving prices and income as variables.).