Consumeri's direct utility function is of the form: %3D where 1, x2 > 0 and a is a parameter. Assume that the consumer's preferences are convex and monotonic. (a) What restrictions must there be on the value of parameter a for the preferences to satisfy the convex and monotonicity properties of the utility function? Explain.
Q: Which of the following statements is correct? a. The demand for future goods is derived from…
A: Utility maximisation refers to the concept that individuals and firms seek to get the highest…
Q: Consider the following consumption dataset over X = R : pi (1, 2, 5) (2, 2, 0.1) 1.5 (0, 0.5, 5) (2,…
A: Here based on the given bundles and respective price levels, we can draw a matrix for different…
Q: Assume an hypothetical consumer faced by the following utility function; U=X^2Y ( squared times y).…
A: We can write the following expression; U=Ksh. 24.2 Now, using the formula for the EV and CV, we get…
Q: Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over her incomes x1,…
A: People typically intend to forfeit small, immediate gains for larger rewards in the future, but they…
Q: Suppose that indifference curves are described by straight lines with a slope of −b. Given arbitrary…
A: Straight-line indifference curve: The straight-line indifference curve has a constant slope…
Q: A person has a 2-period utility consumption function U(c1, c2), with a budget function W = c1+c2/1+r…
A: Given: U(c1, c2), Budget constraint = W = c1+c2/1+r
Q: Utility maximization under constraint Lucas gets utility (satisfaction) from two goods, A and B,…
A: Given information Utility function of Lucas U=25[C-3+4D-3]-4+25 Lets take Price of C=P1 Price of…
Q: (i) Graph the budget constraint for the individual. (ii) Add to your graph the consumer’s…
A: * ANSWER :-
Q: Bob has a utility function U(x, y) = √x1 + 0.8√x2 + 0.64√x3 over his incomes x1, x2, x3 in the next…
A: Hi Student, Thanks for posting the question. As per the guideline, we are providing answer for the…
Q: A maximizing consumer with preferences given by u = x^2+ y^2 allocates 60 dollars of income at pY= 3…
A: Given utility function U=X2+Y2 Budget=$60 Py=3 Px=4 Price falls after a month Px=2
Q: If total utility increases as wealth increases, the first derivative of the utility function is…
A: The first derivative or first order derivation of utility function (TU) is known as the marginal…
Q: What kind of preferences are represented by a utility function of the form u(71,72) = VE + z2? What…
A: The utility is the want satisfying power of the commodity. The utility is the want satisfaction of…
Q: An individual utility function is given by U(x,y) = x·y. Derive this individual indirect utility…
A: Utility refers to the level of satisfaction gained by a person when he/she consumes a good or…
Q: Consider a consumer with preferences represented by a utility function u(r1, 12) = max{r1,72}. The…
A: Indifference curves are the curves that show the different combination of two goods that gives the…
Q: [Indifference Curves] Consider the utility function U(C1, C2) and B 1 In(C1)BIn(C2) 1. Using a…
A: The given equation is : U=ln(C1) + Bln(C2)We know, ln(C1) + ln(C2) = ln(C1*C2)
Q: Show how to construct the reference dependent utility function for two friends Ka and Mary whose…
A: The reference utility function for each individual can be calculated as below For Kate, investment…
Q: A consumer's indirect utility function is given by v(p, Y) = pfpY°, where P1, P2; Y are prices and…
A:
Q: Lucky Larry spends $640 a year on cigars and lottery tickets. The lottery tickets, Good Y are…
A:
Q: Suppose a consumer's utility function is given by U(X,Y) XY. Also, the consumer has $720 to spend.…
A:
Q: “Pertaining to different good characteristics; it is possible to distinguish between three different…
A: A graphical representation of a combination of products that gives a consumer a similar level of…
Q: "Regular-looking" indifference curves - ones you may be familiar with from previous econ courses -…
A: Since the question you have posted consists of multiple parts, we will answer the first three parts…
Q: Derive the Utility Function to find the equation for the indifference curve. U(x, y) = (.6T.5 +…
A: In order to find the equation for the indifference curve from the utility function, we simply…
Q: Solve; a consumer utility function is given as 64q10.5q20.25q30.4 2. derive the second-order…
A: Introduction We have given a utility function of a consumer who is consuming three commodities such…
Q: Consider the lottery that assigns a probability 7 of obtaining a level of consumption CH and a…
A: There are two consumption levels for the lottery : cH , cL Probability of cH = π Probability of cL…
Q: Let the utility function and the budget constraint be as follows: u(x1, 82) = }Inxı + žln¤2…
A: Given utility function U=1/2lnX1+1/3lnX2 Budget constraint M=p1X1+P2X2
Q: Consider a strictly concave and continuously differentiable utility function U(T1, T2) describing…
A:
Q: The preferences of a consumer with utility function U (x1, x2) = (1+x1)(1+x2) are convex. [Note: You…
A: U ( x1 , x2 ) = (1+x1) (1+x2)
Q: Consider a consumer with preferences over two goods, r₁ and 22, that can be represented by the…
A: Optimal consumption bundle is when MUx1 / MUx2 = Px1 / Px2Where, MUx1 = Marginal utility from good…
Q: Suppose the consumer solves the following UMP: max (x1)^2 + (x2)^2 , s.t. p1x1 + p2x2 ≤ w where…
A: U(x1,x2) = max (x1)^2 + (x2)^2 Budget line is given as p1x1 + p2x2 ≤ w where p1,p2 > 0
Q: Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is…
A: Given information U=8*X0.5+Y Budget constraint M=Px*X+Py*Y Py=1
Q: The purpose of consumption is to satisfy and it is assumed that their utility.
A: In an economy, consumption is made by. The households and producing is made by the businesses.
Q: Suppose a consumer is indifferent between the bundles (x1, x2) = (19, 10) and (15, 16), and suppose…
A: Consumer choice refers to the choices that people make about products and services. When we research…
Q: A consumer has Hicksian demand functions h(p1 p2, u)=a()*"ū and h(p1 P2, u)=(1 a)()"ū. Determine…
A: In this question we have to find the Marshallian demand function and slutskey's Equation.
Q: Solve part b and c. There two goods, candy and soda, available in arbitrary non-negative quantities…
A: Consumption bundles are termed as the set of goods and services that are chosen or selected to…
Q: Let u(x) be a utility function that represents % and let f(.) be a continuousmonotonic function.…
A: Monotonic transformation (MT) of a utility function (U) is a transformation by which when a set of…
Q: Show the derivation of the individual demand function for a utility maximizer consumer and explain…
A: Utility refers to the satisfaction derived from consuming given goods and services. Budget…
Q: Assume the consumer is correctly applying the rational spending rule (consumer equilibrium) for…
A: Here, it is given that a consumer is in equal it implies that marginal utility per dollar spent on…
Q: Let u(x) be a utility function that represents the preferences of a household. We say that the…
A: A monotonic transformation (MT) of a utility function (U) is a transformation in which the original…
Q: 3. Over a two-year period, an individual exhibits the following consumption behavior: P P Y Year 1 3…
A: When analyzing a consumer's preferences, there are different terms used to explain different…
Q: Utility functions of a consumer: U = 20x10.4x20.4 Specify: a. marginal utility of each item. b. If…
A: U = 20x10.4x20.4 Marginal Utility of x1 = ∂U/∂x1= ∂(20x10.4x20.4)∂x1= (20)(0.4)x1-0.6x20.4=…
Q: PROBLEM (3) Violet buys pies (x) and champagne (y) with her income of $400 and her utility function…
A: Income:- financial gain is cash earned by someone or a business in exchange for labor, the…
Q: Consider a consumer with utility function u(x1, x2) = a_1x_1^( 2) + a_2x_2^( 2) where a1 > 0 and a2…
A: Given Utility Function U=α1X12+α2X22 Where α1>0 and α2>0
Q: I need asnwers of d,e,f. Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and…
A: We are going to calculate MRS to find the optimal bundle of consumption in both the cases. To…
Q: A consumer's indirect utility function is given by V (p, y) = f(p)y. (a) What is the form of this…
A:
Q: Q.3 A utility function is given by the equation U = 120 x0.7 y0.3 where x is the number of hours…
A: To find the utility maximizing bundle, we apple Lagrange multiplier to maximize utility subject to…
Q: Consider two friends Anna and Elsa whose gains and losses are listed as follows: Anna's investment…
A: We are going to analyze the reference utility function for each individual.
Q: Suppose that consumer has the following utility function: U(X,Y)= X1/2y1/4. Suppose also that Px…
A: Given information: U = X1/2 Y1/4 --------> Utility function Price of X (Px) = 2 Price of Y (Py) =…
Q: Anna's investment is worth $2.5 million (decreased from $3.5 to $2.5 million) Elsa's investment is…
A: Reference Dependence defines as the central principle in the prospect theory and behavioral…
Step by step
Solved in 2 steps
- Consider an economy with two goods, consumption c and leisure 1, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of 7 percent. The con- sumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) = c-3h¹+, where 3 > 0 and p > 0 are parameters. 1+pA 2015 report by the music industry estimated the revenue lost to the industry every yearfrom illegal downloading. In this problem we will derive some of the estimates that may havegone into their calculation (approximately).First, start with the individual consumer’s problem. Suppose a typical consumer has a yearlyentertainment budget of I that they can allocate between music downloads (D) and otherforms of entertainment (E). Consumer preferences are characterized by a utility functionU(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: Youdo not need to solve it or derive first order conditions.)2. A consumer has a utility fuinction given by a) Derive an expression for the two marginal utilities: MU (x1, 22) and MU2 (21, r2). Since AMRS = -YU use these marginal utilities to derive a simple expression for the MRS (r1, 22). b) Optimal choice on the part of the consumer implies MI RS = -. Suppose M 20, p1 = p2 = 1. Show the optimal choice in this case on a well-labelled graph of the budget set. Include an indifference curve consistent with these preferences. c) Now keep income at 20, and pi = 1, but set p2 - 2. Show the optimal choice in this case on a well-labelled graplh of the budget set. Inclnde an indifference curve consistent with these preferences.
- Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?(a) Suppose we have preferences U(X, Y) = 10X²/³ Y¹/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). < (d) What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain.< (e)_From (d) we can show that optimal demands are: X=½ M/PX and Y = ½ M/Px. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands (X*, Y*) and utility if Px = 10, Px= 5 and income M = 1200. < (f)_Suppose Px falls to Px = 8 but Py and M are unchanged (Px = 5 and M = 1200). Calculate the new optimal demands…Suppose that consumer has the following utility function: U(X, Y) = X@Y where 1 > a > 0 and 1 > b>0 are constants. Which of the following is correct? Preferences are convex and indifference curves are bowed inward towards the origin since Law of Diminishing Marginal Utility holds. Preferences are convex and indifference curves are bowed outward from the origin since Lavw of Diminishing Marginal Utility fails to hold. Preferences are concave and indifference curves are bowed outward from the origin since Law of Diminishing Marginal Rate of Substitution fails to hold. O Preferences are convex and indifference curves are bowed inward towards the origin since Law of Diminishing Marginal Rate of Substitution holds.
- (c) If the preferences are concave, will the consumer ever consume both of the goods together?How does a consumer maximizes their utility given that they experience a budget constraint? Explain with graphical illustrations. Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.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?
- Hella the Greek's preferences can be described by the utility function U(x, y) = (x^1/2 + 3^1//2)^2. (a) What is the indifference curve for a utility of 49? (b) By how much does utility increase when Hella increases consumption of good y by one (small) unit, when initially U = 49 and x = 1? (c) Holding utility constant at 49, if initially x = 1, how many additional (small) units of y does Hella have to consume if her consumption of x drops by 6 (small) units?Number of Sodas per day Total Utility Marginal Utilit 1 20 35 3 47 12 4 10 Refer to the table, The marginal utility of the second soda per day is L. (Answer should be in the form of numerical characters, e.g. 20) Enter your answer here2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility.