A utility maximizing consumer purchases two commodities, Q1 & Q2. The consumer’s utility function is described by the following expression: U = Q1 Q2 + Q1 + 2Q2. The prices of the commodities are P1 = $2 and P2 = $5. Suppose the income of the consumer is $51 (a)Form the Lagrangian function that defines the combination of both commodities the consumer could buy subject to the budget constraint imposed by the prices of the commodities and the income of the consumer. (b)Find the combination of both commodities that maximizes the utility of the consumer. (c)Write and evaluate the Bordered Hessian for this utility maximization problem.

Q: Q2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where and…

A: U(x,y) = (x+2)(y+1) Budget Constraint = Px*x + Py*y = I

Q: Gabriel, a student, has a budget of £60 to spend on cappuccinos (good X) and on cups of tea (good Y)…

A: Given,

Q: (a) Suppose the indirect utility function v(p, m) is differentiable. Prove that dv(p, m) av (p, m)…

A: The indirect utility function refers to the maximum attainable utility when prices of concerned…

Q: Suppose the utility function of U(x1, x2) = x11/2x21/2 and the budget constraint of p1X1+p2x2=m.…

A: Utility means satisfaction.  Higher the utility, higher is the satisfaction.  The budget constraints…

Q: Suppose a consumer’s preferences can be represented by the utility function U(X,Y) = Min (2X,Y).…

A: Utility function: U = Min (2X, Y) --------------------- Budget constraint: Price of good X (Px) = $2…

Q: A consumer derives utility from good A and B according to the following utility function: U(A, B) =…

A: Utility maximization problem: With the given prices and income, a consumer chooses his consumption…

Q: Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility…

A:

Q: utility function

A: 1. Lagrangian Method:Define the Lagrangian function:Solve the system of equations for the…

Q: Prove that if u is a reasonable utility function, then u(w) — u(w − h) > u(w+h)- u(w) for any w > 0…

A: A reasonable utility function assigns numerical values to outcomes based on personal preferences,…

Q: Milo spends £27 on stamps (S) and maple candy (C). His preferences for these goods are given by the…

A: Given ,  Milo income = 27  Utility function : U = min { S , 3C  }  Price of Stamps = 1.1  Price of…

Q: Consider the consumer whose tastes and preferences for (X) and (Y) can be characterized by the…

A: The utility function can be written as follows: The budget constraint can be written as follows:

Q: Helen buys 2 goods: clothing (x) and food (y). One unit of clothing costs $15, while one unit of…

A: Given Information: One unit of clothing costs Px=$15 one unit of food costs Py=$5 budget (I) = $100.…

Q: For the utility function U = (Qx0.5+Q,0.5)2 and the budget 167 = 10Qx+8Qy find the CHANGE in optimal…

A: Utility functionU = (Qx0.5+Qy0.5)2Budget Constraint167 = 10Qx + 8QyTherefore , Price of x = 10Price…

Q: Problem 1 Consider the following utility function: U(x₁, x₂) = (x₁)²x₂. Task 1 : Suppose a consumer…

A: The utility function is The price of good 1 is 2The price of good 2 is 3The income is 18.

Q: Suppose a consumer had a utility function given by: U= 2X + 5Y. If the price of Good X (Px) is $6…

A: Utility maximization refers to the process by which individuals or firms allocate their resources in…

Q: Assume there is consumer, his utility function is U(x,y)=y/(100-x). If px = 1, py = 1, please show…

A: Utility function U (x, y) = y/(100-x)    .... 1) (MUx) / (MUy) = Px /Py.…

Q: find the utility-maximizing consumption function subject to the budget constraint

A: For the utility maximising consumption bundle the basic principle is that we equate the rate at…

Q: A consumer has income I and faces prices p1 and p2 for goods 1 and 2. The corresponding quantities…

A:

Q: alculate the marginal rate of substitution (MRS12) for the following utility function: U(q1,q2)=…

A: Marginal rate of substitution refers to the slope of an indifference curve. It is calculated as the…

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: Suppose a consumer had a utility function given by: U = X³Y. If the price of Good X (Px) is $6 and…

A: Utility maximization refers to the process by which individuals or firms allocate their resources in…

Q: Aji's utility function for Blueberry (b) and Raspberry (r) is given as U = f(b, r); Budget…

A: Answer: Given, Budget constraint: 100=4b+5rWhere,b=number of blueberryr=number of raspberry (1).…

Q: Maya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies…

A: a) When the price of CCC (chocolate chip cookies) is $1, which is the same as the price of donuts,…

Q: Suppose a consumer has preferences represented by the utility function U(X,Y) = X2Y Suppose PY = 1,…

A: A graphical representation of a combination of products that gives a consumer a similar level of…

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: A consumer can consume three goods, x₁, x2, and x3. In the markets where she buys them, she is a…

A: Utility, in economics, implies the usefulness or happiness a consumer can get from a service or…

Q: Given the total utility function for a consumer, consuming two goods is U = x+2y + xy +2 the prices…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.