Kindly solve these for me
9. Assume Alice preferences satisfy the axioms of the expected utility theorem with the utility function u(x) representing her preferences over outcomes x. Which one of the following statements is false? A. Alice preferences are also represented by the function u(x) - 100 B. Alice preferences are also represented by the function 3 - 2u(x) C. Alice preferences are also represented by the function Su(x) D. Alice preferences are also represented by the function u(x)2Consider an individual making choices over two goods, x and y with initial prices px= 5 and py= 2, with income =100: a If the individual's preferences can be represented by the utility function u = 4x- 2y; find the income substitution and total effects of a decrease in the price of x to px= 3. bl if the individual's preferences can be represented by the utility function u = min(4x,2y); find the income substitution and total effects of a decrease in the price of x to px= 3.1. (a) Use the Intermediate Value Theorem to show that the equation - sin (x) + sin(x) =-1 has at least two distinct real solutions on (0, ce). Justify your answer. (b) Let ( fa)=2 be the sequence of functions defined by: 1 -nex, fu( x) = 0. 2 it xe [ 3. 1 ] (1) Find the pointwise limit of the sequence of functions (.),2 Does the sequence ( ,), , converge uniformly on [0. 1| to its pointwise limit? Justify your answers Let a. B E N. and f : 8 - R be the function defined by: B (sin (;))" cos (!). f( x) = For cr EN and B > 2, show that function / is differentiable on R. and give the value of f(x) for allre R. (1) For de N and B - 1, show that / is not differentiable at 0.PLEASE PROVIDE DETAILS EXPLANATION #2. Consider an individual making choices over two goods, x and y with prices px and py, and who has income I: (a) If the individual preferences can be represented by the utility function u(x; y) = 3x + 2y2, what is the marginal rate of substitution MRSx;y? Is the utility function homothetic? Graphically illustrate a typical indierence curve and explain how you know the shape. (bj if the individual preferences can be represented by the utility function U(x y) = 2xy2, what is the marginal rate of substitution MRSx:y? Is the utility function homogeneous, and if so, to what degree? Graphically illustrate a typical ina derence curve and explain how you know the shape.1. The production function for ACME WIDGETS is given by Q = 30 K^0.65 L^0.25 , where Q is the number of widgets ACME produces in a month, K is the number of units of capital input and L is the number of units of labor input ACME uses to produce their widgets. The price per unit of capital input is p K = $ 4 , 000 and the price per unit of labor input is p^L = $ 2, 000. ACME's minimum cost of producing 900 units/month is a 148212 b 260787 c 278918 d 206696 2. This continues the previous problem. ACME's marginal cost is Group of answer choices Decreasing as output increases, There is not enough information to tell how the firm's marginal cost is behaving ncreasing as output increases Constant as output increases
