Consider a consumer with the utility function u(x,y) = r*y, where a and b are both strictly positive real numbers. The consumer's income is m, the price of good x is p, and the price of good y is py- (1) Verify that this consumer's preference satisfies local non-satiation and strict con- vexity. (2) Write down the consumer's utility maximization problem. (3) Setup the Lagrangian for the utility maximization problem and find the first-order conditions.

Q: Amy is a chocolate lover and has a total of 50 dollars to spend this week. The price of a certain…

A: Given Utility function U(q)=q+50-pqq∈0,50PTotal budget=50Price of q=50

Q: 7.1. Consider preferences defined over the nonnegative orthant by (1, 12) ► (yı, 42) iff x1+I2 <…

A:

Q: 1. Consider utility function Ux1,x2=x,0.5x20.5 for x1<0 and x2<0.Show that the function satisfies…

A: The utility is the capacity of good that satisfies human wants.

Q: Suppose that a consumer has the utility function u(x1,x2) : quantity of good i consumed, i = 1, 2.…

A:

Q: You are given the following utility function and price of commodities q1 and q2: U =…

A: Utility is maximized at the point where indifference curves are tangential to the budget constraint…

Q: 1.a Assume that a person’s utility function is given by the following function: ??=3?^(2/3)?^(1/3)…

A: Given, U(X,Y) = 3X2/3Y1/3 Price of X (PX) = £3 Price of Y (PY) = £3 Budget (M) = £45 Budget line…

Q: A consumer has the utility function u(x, y) = xy and faces the budget constraint 2x + y = 100. Find…

A: We are given: Utility function : u(x,y) = xy  -- (1)Budget equation : 2x + y = 100 =&gt; y = 100 -…

Q: Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y IS S1…

A: Given: Px =2Py = 1UA(X, Y) = X0.5Y0.5UB(X, Y)= X0.8Y0.2MA = 100MB = 300   (a) Utility maximization…

Q: Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y),…

A: U(x,y,z)=x0.5y0.5(1+z)0.5 where Px = 1 Py = 4 Pz = 8 Income = 8

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: You have £20 per week to spend, and two possible uses for this money: telephoning friends back home,…

A:

Q: ;) Given preferences represented by the utility function u(x1, x2) = min{3x1, x2}. a) Write down the…

A: a) The given utility function is: U= min( 3x1, x2) This represents the utility function of perfect…

Q: Assume an individual's utility from consuming good #1 and good #2 is given by the following…

A: From the utility function, we can infer q1 and q2 are perfect complements and are consumed in fixed…

Q: Consider a consumer who purchases two goods, x and y. The consumer’s utility function is U(x, y) =…

A: The budget constraint of the consumer shows the different combinations of two goods that an…

Q: A consumer's indirect utility function is given by v(p, Y) = pfpY°, where P1, P2; Y are prices and…

A:

Q: You have k20 per week to spend and two possible uses for the money: telephoning friends back home…

A: The utility maximization condition is given as MUx/MUy= Px/Py where MUx is the marginal utility of X…

Q: An agent has utility u(x1, x2) = (x-11+x-12)-1for goods x1 and x2. The prices of the goods are p1…

A: Given: An agent has a utility of: U(x1,x2) = (x1-1 + x2-1)-1 The prices of goods are = p1 and p2…

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: A consumer utility function is U=(x1,x2) Where X1 is the quantity of good 1 that is bought, X2 is…

A: Optimality of utility is attained where utility is maximized subject to budget constraint.

Q: Suppose a consumer had a utility function given by: U = XY². If the price of Good X (Px) is $6 and…

A: Suppose a consumer had a utility function given by: U = X * Y ^ 2 . If the price of Good X (Px) is…

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: 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: Assume the utility U of a pair of goods x and y can be determined by U(x, y) = 4xy. Furthermore,…

A: Given Information U = 4xyBudget constraint x2 + y2 = 1

Q: Consumeri's direct utility function is of the form: %3D where 1, x2 > 0 and a is a parameter. Assume…

A: Solution- ui(x1,x2)=x1α x2(12-α) To be convex preferences, uxi11 &lt; 0 Now, diff. the utility…

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: A consumer utility function is U = 1 log x1 + log x2. His budget constraint is given by 2x1 + 4x2 =…

A: The consumer is in equilibrium when he gets maximum satisfaction out of his expenditure. The…

Q: Consider a consumer whose preferences satisfy monotonicity. Since the consumer prefers more to less,…

A: The consumer preferences would result in an increase in the utility which would result in an ever…

Q: Suppose a consumer has the following utility function: U(x1,x2) = alnx1 + (1-a)lnx2. The price of…

A: We have  Ux1, x2=alnx1+1-alnx2 When a= 1/2 or a=0.5 Ux1, x2=0.5lnx1+0.5lnx2             ............…

Q: What is the logarithmic transform of the utility function U= , given the budget constraint Pa, 21 +…

A: We have to find logarithmic transform of the utility function.

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: 3 1. A consumer has the utility function U(x,y) = 2x y where x and y represent the quantity consumed…

A:

Q: Let Utility be given by    U(x,y)=x^2 y^2   With a budget contraint   p_x x+p_y y=Y     Let px = 10…

A: To maximize the utility function(U), the marginal rate of substitution(MRS) should be equated with…

Q: Consider a consumer whose preferences are represented by a utility function u(x, y) = a0.5y5 Are…

A: The utility function can be defined as the measure of a group of goods and services preferred by…

Q: Suppose that consumer uses 1 units of X and 7 units of Y always in fixed proportion. Then, what…

A: There are two goods, i.e., X and Y A consumer uses 1 unit of X and 7 units of Y in a fixed…

Q: Find the demand functions of the consumer who has a Cobb Douglas utility function U(x,y) = Axayb…

A:

Q: sume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is…

A:

Q: Suppose that the preferences of the consumer are represented by the following functions of utility:…

A:

Q: Consider a consumer with the utility function U(X,Y) = In(vX + vY) and suppose that the prices of…

A: Given prices and income, the budget constraint is given by pXX+pYY=I⇒2X+4Y=120 To solve the utility…

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: Consider a consumer whose preferences are represented by a utility function u(a, y) = a0.5 5. Are…

A: Utility function can be defined as the measure for a group of goods and services preferred by…

Q: Consider the problem of a consumer who must choose between two types of goods, good 1 (2₁) and good…

A: Given function U=X1+X2Price of X1= P1Price of X2=P2Consumers income=M

Q: Given the following utility functions, check if the utility function is homogeneous and if MRS is…

A: The marginal rate of substitution (MRS) in economics is the quantity of a good that a consumer is…

Q: A consumer consumes pizza and soda always in the fixed proportion of 3 slices of pizza (x) with 2…

A: We are going to represent the utility function for perfect complement and its maximisation to answer…

Q: A consumer has a utility function given by lnU =5linx subscrip1 +3lnx subscript 2 if the budget…

A: Answer - Need to find- optimal quantity of the two commodities Given in the question- lnU =5lnx1…

Q: A person with utility function Ux, y) = 5+ y+ 2x has nonconvex preferences. True False

A: Answer:- TRUE

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: 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 --------&gt; Utility function Price of X (Px) = 2 Price of Y (Py) =…

Q: Consider a consumer whose preferences are given by the utility function U (x, y) = (x + 1)² (y +…

A: