1. clara's utility function is u(x, y) = (x + 2)(y +1). a) write an equation for clara's indifference curve that goes through the point (x, y) = (2, 8). b) suppose that the price of each good is one and that clara has an income of 11. write an equation that describes her budget constraint. c) find an equation the describes clara's mrs for any given commodity bundle (x, y). d) use the equations in parts b) and c) to solve for clara's optimal bundle( hint use the fact that at clara’s optimal choice = mrs) e) find clara’s demand function for good x (i. e. find x(px, py, m). 2. consider bridget, who has preferences that can be described by the function u(x, y) = 5ln(x) + y. find bridget's demand functions for x and y.

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step-by-step explanation: ; )

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation: