Suppose there are two goods that a consumer can consume only in nonnegative quantities, and let a be defined by x y if and only if x1 +x2 < y1 + y2. Is è locally nonsatiated? b) Will this consumer spend all of his or her income?
Q: Suppose a consumer’s preferences over two goods x1 and x2 are given by u = root(x_1 x_2). Her…
A: Answer: Given, Utility function: u=x1x2 Price of good 1 = p1 Price of good 2 = p2 Income = M The…
Q: Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z).…
A: In microeconomic analysis of utility maximization, a consumer attains his equilibrium where the…
Q: 7.1. Consider preferences defined over the nonnegative orthant by (1, 12) ► (yı, 42) iff x1+I2 <…
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Q: Consider a consumer with the following quasi-linear utility function Assume that the consumer faces…
A: *Hi there , as you have posted question with multiple sub parts , following are guidelines we can…
Q: Sukai consumes only apples and tomatoes. Her utility function is U(x, y) = X2 y where x is the…
A: GIVEN Ans. Utility Function, U(x, y) = x^2 y^8 Income ( M) = $320 the price of apples( Px) = $4…
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Q: A consumer spends all her income of K120 on the two goods A and B. Good A costs K10 a unit and good…
A: In economics, the term "utility" refers to the sense of well-being that comes from using a product…
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Q: An agent consumes quantity (x1,x2) of goods 1 and 2. Here is his utility function: U(x1, x2) =…
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Q: Jane has utility function u(x,y)=x4y5. The price of x is px, the price of y is py, and Jane’s income…
A: Given- U=X4Y5 MUx can be found by differentiating U in terms of xSo, MUx= 4X3Y5MUy can be found by…
Q: Ann consumes only cookies and muffins. At her current consumption bundle, her marginal utility from…
A: A buyer optimizes his/her utility measured in utils when the ratio of marginal utility of last unit…
Q: Suppose a consumer's utility function is given by U(X,Y) XY. Also, the consumer has $720 to spend.…
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Q: 1. Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza…
A: b) The consumers problem is: max u(B,Z) =B1/2+4Z1/2B+2Z=45And the Lagrangian function required…
Q: Question 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of…
A: As given utility function is u(x1,x2) = αlnx1 +lnx2 Where α>0
Q: Given a consumer has a money budget M = 360 and utility function U(X, Y)=X^(3/4)Y^(1/4). If she…
A: The condition which is needed for the utility maximization is: MUX/MUY = PX/PY where, MUX and MUY…
Q: PLEASE HELP ME ANSWER IT AS FAST AS YOU CAN Dalal consumes only two goods for lunch and dinner:…
A: Note: Since the question contains more than three subparts, we are going to answer first three…
Q: A consumer has utility function U(q1, q2) min{4q1, q2}. Find the consumer's (Marshallian) %3D demand…
A: Given Utility function U(q1,q2)=min{4q1,q2} ... (1) Consumer income =y Price of good 1 =p1…
Q: Given the following utility function: U = 5X + 10Y and marginal utilities: MU, = 5, MU, = 10 A…
A: U=5X+10Y MUx=5 MUy=10 Px=2 Py=1 Consumes(X,Y)=(16,9) MRS is the marginal rate of substitution. It is…
Q: Consider the following utility function: u(x1,x2) = x1 + x2. (A): i) Restate the consumer problem.…
A: * Hi there , as there are multiple questions posted . Following our guidelines we can only solve the…
Q: 1. An agent consumes quantity (x1,X2) of goods 1 and 2. Here is his utility function: U(x1,x2) =…
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Q: Lucy consumes only scoops of ice-cream (x) and cones (y). Moreover, she insists on consuming these…
A: Given information; Lucy consumes two goods, i.e., only scoops of ice cream (x) and cones (y) Her…
Q: The consumer's utility function is u(x1,x2) = x1 x2 Graph her budget constraint for P1 = 3, P2 = 2…
A: Budget constraint shows the different possible combination of consumption of goods and services…
Q: Suppose Ming spends his entire income on two goods, X and Y, has "standard-looking" indifference…
A: Normal Goods: Normal goods are those goods whose demand is directly related to income. If income…
Q: Assume that Rossi consumes only bananas and avocado. Fortunately, she likes both goods. The…
A: X1 represents consumption of bananas per week X2 represents consumption of avocado per week.…
Q: Carol has very weird preferences. She only cares about quantity. When evaluating a bundle, Carol…
A: Carol is indifferent between two bundles:- Bundle 1:- 5 eggs and 1 dumpling Bundle 2:- 4 eggs and 5…
Q: A consumer has a Cobb-Douglas utility function and consumes two goods x and y. If the price of good…
A: In economics, Cobb-Douglas utility function is widely used to show the ordinary consumer…
Q: A consumer's utility function is -a u = x1x², where ₁ and 2 are the quantities consumed of goods one…
A: The total level of satisfaction that an individual derives from the consumption of good is referred…
Q: Consider an individual with the following utility function, U(x, x) = ax?x5. The current price of x,…
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A: Utilty is defined as the satisfaction which the consumer gets by consuming the homogeneous units of…
Q: Consider an economy with two goods t = 1, 2. Whenever an individual consumes xị units of good 1 and…
A: Marginal rate of substitution between good 1 and 2 can be defined as MRS =dUdX1dYdX2 = 1X1δX2 =…
Q: A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and…
A: The budget line represents the combinations of two goods that a consumer can purchase with the help…
Q: Suppose an individual is currently spending all of their income on a bundle of books and pizza, but…
A: Good marginal utility price in $ $ marginal utility Book 6 12 6/12 = 0.5 Pizza 3 7 3/7 = 0.43…
Q: Suppose a consumer purchases food X and clothing Y. The utility function of the consumer is given…
A: Consumer purchases food X and clothing Y Utility function of consumer; U(X,Y)=XY+5Y Income of…
Q: John has preferences for food F and clothing C described by a utility function . Suppose that food…
A: Given: The food costs = $1 a unit The clothing cost = $2 a unit John spends on food and clothing =…
Q: Suppose we are able to model the total utility function for the consumption of two goods, good x and…
A: Utility is maximized when slope of indifference curve given by ratio of marginal utilities and slope…
Q: A consumer is maximising her utility function: U(r, y) = (105 + y0.5), subject to the budget…
A: Given information: Utility maximizing function: U(x,y)=x0.5+y0.52 Budget Constraint : 4x+2y=108
Q: By definition, a budget constraint shows the consumption bundles that a consumer can afford. Assume…
A: The amount of goods that a consumer can purchase over a given period of time is limited by the…
Q: Suppose the representative consumer has the (quasilinear) utility function: U(x. y) = ax + In())…
A: (a) Quasilinear means possessing some properties of linearity but not linear in all. In the given…
Q: Jane's utility function is U=X^2Y^8 , with marginal utilities being MUX=2XY^8 and MUY=8X^2Y^7.…
A: Answer: Given, Utility function: U=X2Y8MUX=2XY8MUY=8X2Y7PX=1PY=3I=120 The budget constraint of this…
Q: Which of the following is not a required characteristic for a function U(.) to be considered a valid…
A: Utility function: A way of assigning a number toevery possible consumption bundle such that…
Q: A consumer's indirect utility function is given by V (p, y) = f(p)y. (a) What is the form of this…
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Q: Assume the following expression summarizes an individual's demand for good #1: qª (P1, P2, Y) = 10 –…
A: Given Individual demand q1p1,p2,y=10-p1+2p2-y ........ (1) p1 = 8 and p2 =5 y= 10
Q: Mary's preferences over X and Y correspond to the following utility function: U(X,Y) = XY³. Suppose…
A: Consumer will maximise its utility at a point where marginal rate of substitution is equal to price…
Q: 1 Consider a consumer who consumes only two goods, z1 and z2. His utility function is u (1, 2) = In…
A: Utility function is given as:- U(z1,z2) = lnz1+z2 Price of z1 = $2 Price of z2 = $4 Income = 100
Q: A consumer's utility function is given by u (r_y) := r'/2y!/2 for any nonnegative r and y,…
A: Given information U = x1/2y1/2 Price of x good = Px Price of y good= 1 cent=$0.01 Income of the…
Q: The preferences of a typical Californian can be represented by the following utility function: U…
A: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) α=0.25 U (x1 , x2 ) = 0.25 ln(x1) + 0.75 ln(x2)
Q: Lisa consumes only pizzas (P) and burritos (B). Her utility function is U = P0.5B0.5. The price of…
A: Utility function: U = P0.5B0.5 PP = 10 (Price of pizza)PB = 5 (Price of burrito) In equilibrium MRS…
Q: Consider the following utility function: U= 100x 50,0.50 %3D A consumer faces prices of P, = $2 and…
A: U=100X^0.5Y^0.5 Px=$2 Py=$1 MRS=1.83 MRS is the ratio of marginal utilities of the two goods In a…
Q: Consider a consumer whose preferences are given by the utility function U (x, y) = (x + 1)² (y +…
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- Would you expect total utility to rise or fall with additional consumption of a good? Why?Consider a consumer with M = $120 to spend (income) and faces prices PX = $15 and PY =$5 for goods X and Y. Her utility function is U(X, Y) = X1/2 + Y1/2.a Carefully. express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the other…Total utility is maximized in the consumption oftwo goods by equating thea. prices of both goods for the last dollar spenton each good.b. marginal utilities of both goods for the lastdollar spent on each good.c. ratios of marginal utility to the price of bothgoods for the last dollar spent on each good.d. marginal utility of one good to the price ofthe other good.
- PLEASE HELP ME ANSWER IT AS FAST AS YOU CAN Dalal consumes only two goods for lunch and dinner: risotto (R) and lamb machboos (M). Dalal’s utility function isgiven by U(R,M) = R + 4M. Suppose that a risotto dish costs 3 KD and that a dish of lamb machboos costs 6 KD.Dalal has 300 KD a month to spend on her lunch and dinner meals. a. How many risotto and lamb machboos dishes will Dalal buy each month if she maximizes utility?Dalal’s brother, Jassem, wants to make her happier and is considering two options: giving her a 60 KD gift card that can only be spent on risotto from one of the Italian restaurants or giving her some cash money.If Jassem chooses to give Dalal the 60 KD risotto gift card:b. How many risotto meals can Dalal add to her optimal basket? c. What utility level will Dalal get given her income and the risotto gift card?Suppose that Jassem instead chooses the second option and promises Dalal to raise her income to the level thatensures making her as happy as the first…Suppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M =$90 to spend and the prices of goods X and Y are PX = $15 and PY = $6 . a. Carefully express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the…A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.
- (a) A consumer has utility u(x,y,z) = ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz=1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? (HINT: MUx = 1/x, MUy= 2/y, MUz = 3/z and remeber the "equivalent bang for the buck" condition). (b) Forget about (a). Suppose you have t= 29 hours in total to spend on 3 projects X,Y and Z to make some money. If you spend x hours on project X, you make 2 sqrt(x) dollars; If you spend y hours on project Y, you make 3 sqrt(y) dollars; If you spend z hours on project Z, you make 4sqrt(z) dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x? on y? on z?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?Given an individual’s current consumption patterns, we know that the person is consuming in such a manner that he is maximizing his satisfaction. Given a decrease in the price of one of the goods he normally purchases, what will happen to the consumer’s total satisfaction and to the marginal utilities connected with the consumption of this particular good. a) His overall satisfaction will increase, but his satisfaction from the last unit consumed of the good with a decreased price will decrease. b) His overall satisfaction will decrease and his satisfaction from the last unit consumed of the good with a decreased price will decrease. c) His overall satisfaction will increase and his satisfaction from the last unit consumed of the good with a decreased price will increase. d) His overall satisfaction will decrease and his satisfaction from the last unit consumed of the good with a decreased price will increase. e) We cannot tell about the changes in his total utility or his marginal…
- Suppose the linear demand curve for shirtsslopes downward and that consumers buy 500 shirts per yearwhen the price is $30 and 1,000 shirts per year when the priceis $25.a. Compared to the prices of $30 and $25, what can you sayabout the marginal valuation that consumers place on the300th shirt, the 700th shirt, and the 1,200th shirt they mightbuy each year?b. With diminishing marginal utility, are consumers derivingany consumer surplus if the price is $25 per shirt? Explain.c. Use a market demand curve to illustrate the change in consumersurplus if the price drops from $30 to $25.A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.a) Determine this consumer’s current utility level. b) Computetheconsumer’smarginalutilitiesofgoodsXandY. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X.d) Determine this consumer’s optimal consumption of both goods. e) By how much does the consumer’s utility increase when she consumes the optimal bundle?consumptionA consumer's budget constraint is given by 500 = 40G + 10D, where G is ice cream in liters and D is drink in liters. The consumer thinks that a liter of ice cream is a perfect substitute for 3 liters of drink. Which statements are then correct?Select one or more options: a-2 liters of ice cream and 42 liters of drink are on the budget line b-The optimal choice is to consume 3 times as much drink as ice cream c-The optimal choice is to only consume ice cream d-0 liters of ice cream and 50 liters of drink are on the budget line
