7 Derive Marshallian/Ordinary Demand for both x utility functions a) U(x, y) = min[1x, 6y] 。) U(x, y) = 30/n(x) + y MUX=30 MUy = 1 c) (/(x, y) = 4x +3v MU₁ = 4 MU₁, = 3
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- A consumer has utility function U(x1, X2, X3, X4, X5, X6, X7) = min{/x1x2, /X3X4, VX5X6X7} Find the demand function. 3)1. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects to be found below. (b) u(x1, x2) = x1 + x2. (c) u(x1, x2) = x1x2. (d) u(x1,x2) = min {x1,x2). (e) Rank the substitution effects and the income effects found above by their magnitude. To what extent do they conform to your guess?Suppose we observe that an individual's demand for good 1 is: 1/(2p,+p2) (where I- income). From this we can conclude that: Goods 1 and 2 are perfect complements O The price of good 1 is higher than the price of good 2 Two answers are correct O Goods 1 and 2 are perfect substitutes Three answers are correct No answer is correct Goods 1 and 2 are normal goods O These goods may be perfect substitutes or perfect complements, it depends upon the utility function
- I am unsure the direction the utility functions would go in , with this specific scenarioSuppose you have the following indirect utility function: V(Pa, Py, I) = In PxPy What are marshallian demands for x and y? I (a) (9x9y) = (22) (b) (9,9y) = (In, In 2) (c) (9, 9y) = (exp(2p/py), exp(2ppy)) I (d) (9x, gy) = (2pr+py' px+2py) What is the expenditure function for the associated expenditure minimization problem? (a) E(pa, Py, U) = (P + Py) ln(U) (b) E(pa, Py, U) = √exp(U)Papy (c) E(pa, Py, U)= (p²+p²) In(U) (d) E(pa, Py, U) = exp(U)²papy What are the individual's Hicksian demands for goods x and y? (a) (h₂, hy) = ((BU)¹/², (PU) ¹/²) (b) (ha, hy) = (RU, DU) (c) (ha, hy) = ((2 exp(U))¹/², (exp(U))¹/²) -1/2 (d) (hx, hy) = ((P₂PzU)−¹/², (P₂PzU)-¹/2) Are x and y complements or substitutes?Refer to the graph below Quantity of Y 160 0 Multiple Choice The consumer's income is $1,000 Why doesn't the consumer choose the combination at point B O Quantity of X 200 O The marginal utility of Y exceeds the marginal uplity of X O The consumer is willing to give up more X for an additional unit of Y than must be given up given the relative prices of X and Y. The marginal utility per dollar spent on X exceeds the marginal utility per dollar spent on Y The consumer is willing to give up more Y for an additional unt of X than must be given up given the relative prices of X and Y
- 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)A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizzaQuestion One ) Zabron has preferences > for Champagne (good 1) and Wine (good 2) defined by. (x1, x2) > (21, 22) e min (x, x2) 2 min (z1. z2) and max (x, x2) 2 max (z,, 2) Are Zabron's preferences complete? Transitive? Locally Non – satiable? Convex? Justify your answers and draw the No-worse-Than, No-Better-Than and the Indifference set of a representative bundle. (i) Suppose that Zabron's preferences > can be represented by a continuous utility function. Show that > satisfies Axioms 1 (Completeness), 2 (Transitivity) and 3 (Continuity).
- Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.9) The satisfaction obtained by a consumer of good 1 and good 2 can be represented by the utility function u (X1, X2) = X1 + 2X2 If the price of good 1 is p1 = 2 and the price of good 2 p2 = 3 its income is positive, then Choose one: A)The consumer will demand a positive amount of good 2 and will not demand anything good 1 B)The consumer will demand) a positive amount of good 1 1 will not demand anything good 2 C)The consumer will demand a positive amount but not necessarily the same amount of both goods. D)We cannot make any statement as to the quantity demanded of each good E)The consumer will demand an equal (positive) amount of both goods