Consider the following utility functions. G(x,y) = x² + 3y² H(x,y) = (x+1)¹/2 + y + 1 L(x,y) = x ey U(x,y) = ln(x) + y² W(x,y) = 100 x - 4x² + 3 y Z(x,y) = (x)¹/2 + y Which function or functions have strictly convex indifference curves (at every point where x>0 and y>0)?
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- When utility function U(q1, q2)=min{ 34.6 q1, 17 q2} and q1= 33 and q2= 60 are given, find utility level consumer gains?First household m=$2,500 per month, spends $125 dollars per month on electricity. Second household m=$10,000 per month and spends $200 per month on electricity. p1=0.1 and p2=1 x1=consumption of electricity and x2=everything else The preferences over electricity and other goods is described by a Cobb- Douglas utility function. What are the parameters of the utility function for each of the two households?Ann's utility function is U = q1q2/(q1 + q2). Solve for her optimal values of q1 and q2 as a function of p1, p2 and Y.
- given this utility function 95x10.3x20.2x30.25 first the first, second and cross order patial derivative with respect to each of the derivatives x1 x2 x3 what is the total utility derive if x1=24 x2=15 x3=5I am unsure the direction the utility functions would go in , with this specific scenarioSuppose the utility function for a consumer is given by U = X + Y, where X and Y are a consumer's consumption of goods X and Y. Which of the following bundles does this consumer find indifferent between 10 units of X and 5 units of Y? You Answered a. 4 units of X, 10 units of Y b. 2 units of X, 13 units of Y c. 5 units of X, 7 units of Y d. 8 units of X, 8 units of Y
- Describe the two approaches of utility analysis !What kind of preferences are represented by a utility function of theform u(x1, x2) = √x1 + x2? What about the utility function v(x1, x2) =13x1 + 13x2?A consumer has the following utility function: U(X,Y)= 400X2/5Y3/5 Suppose that the price of a spa day (x) is £200 and the price of a city break (y) is £300 Find the number of spa days and city breaks that minimise expenditure if 12,800 units of utility are obtained. Also calculate the consumer's minimised expenditure
- Which of the FF. statements is correct regarding the preference of the consumers when the income of the consumer can only be spent between apples and oranges? Assume that apples are written on the vertical axis while oranges are written on the horizontal axis A. when the consumer has few oranges, he is willing to trade more apple to get another orange B. when the consumer has so many oranges already, he will only exchange less apples for an orange C. the declining slope of the indifference curve shows the marginal value of oranges is declining D. all are correct E. none is correctFor the following utility function find the MRS at (x, y) = (2, 3) a) U(x, y) =2x +y b) U(x, y) =x^3 y^2 c) U(x, y) =min(x, 2y)A consumer prefers to consume two commodities in fixed proportions. Specifically, she prefers to consume 1 unit of x2 and 4 units of x1 at the same time. Represent her utility function and find the most preferred and affordable consumption bundle for prices p1 and p2