In consumer theory, it is taught that the slope of an indifference curve (a curve that shows combinations of x and y that yield the same level of consumer satisfaction) is the negative of the ratio of the marginal utilities. This slope is known as the marginal rate of substitution (MRS) and the formula is: OU(x, y) Ux(x, y) MRS = Ox = OU(x, y) Uy(x, y) dy Specify the MRS if U(x, y) = x0.4 ,0.6 [Hint: find Ux first, then Uy , and finally plug it into the MRS formula.] O 0.4 MRS = - -0.4 0.6 X O 0.4x-0.6 MRS = 0.6y-0.4 O 410.6Consider the Cobb-Douglas production function: Y = F(K, L) = K1/3 1 213 Assume capital and labor are greater than zero (i.e., K > 0 and L > 0 ). Which of the following statements is true? O aY OL = FL(K, L) = 2K1/3 1-113 . As labor increases, ceteris paribus, output increases. O aY OL = FL ( K, L) = =1/3 1 1/3 As labor increases, ceteris paribus, output decreases. O aY OL = FL( K, L) = ~K1/3 1-113 As labor increases, ceteris paribus, output increases. O aY OL = FL( K, L) = 2K1/31-113 + 1 As labor increases, ceteris paribus, output decreasesQuestion 7 3.5 pts Consider the utility function: U = U(x, y) = 3x"'+4yB What is the total differential of the utility function? O dU = (3ax*-1) dx + (4ByB-1) dy O du = (3axa-1 ) + (4By B-1 ) O du = (3xx*-1 ) dx O dU = (3ax" ) dx + (4By?) dy.m..- \"n. Question 3 3.5 pts Consider the function, z= f(x,y) . One way to denote the partial derivative of f with respect to x is: airway) dx "K f'