How many independent variables are there in a general utility function of the form U=h(x,y)Question 3Select one:a.3b.4c.2d.1

Consider the following utility functions (in a world with Good X andGood Y ):I. U (x, y) = √xyII. U (x, y) = 4x + 3yIII. U (x, y) = min{x, y} (That is, U (4, 3) = 3, U (1, 1) = 1, U (2, 3) = 2, etc.)IV. U (x, y) = √x + y(a) Fill out the last 3 columns of Table 1. “MRS” stands for Marginal Rate of Substi-tution here. (You would need to copy this table into your answer.)(b) Fill out the the first 4 columns of Table 1 with a Yes/No entry for each cell. Justifyyour answers.(c) Do all utility functions display diminishing MRS? Justify your answers.Note: For the utility function U (x, y) = min{x, y}, calculus cannot be used. How-ever, think about the concept of MRS as how much of y you are willing to give upfor a bit more of x, as represented by the steepness of the indifference curve at apoint. Can you find some value for MRS in this case?(d) Sketch an indifference curve for each of the above utility functions.Table 1. Question 1: Properties of Common Utility FunctionsMonotone Strongly Monotone Convex Strictly Convex MU x MU y MRSI. No 12 x 12 y − 12II. Yes −4/3III. YesIV. Yes Yes1

Suppose thatF (x, y) = g(u(x, y), v(x, y))with u(x, y) = x2 and v(x, y) = h(x, y) − x. Furthermore suppose thath(1, 1) = 2, hx(1, 1) = 3, hy(1, 1) = −2, g(1, 1) = 6, gu(1, 1) = −4 andgv(1, 1) = 5. Determine the partial derivatives Fx(1, 1) and Fy(1, 1).

Are the preferences represented by the utility function U (x, y) = 3x+2y homothetic?

Mukesh spends all his $100 weekly income on two goods, X and Y .His utility function is given by U(X , Y ) = XY . If PX = 4 andPY = 10, how much of each good should he buy?

Use the following table to answer the question below.  Units Consumed Total Utility Marginal Utility0 0 —1 W 202 35 X3 Y 104 40 Z The value for Y isMultiple Choice25.30.40.45.