We have described the slope of an indifference curve as the marginal rate of substitution between the two goods. Supposing that (:2 is plotted on the vertical axis and (:1 plotted on the horizontal axis, use the implicit function theorem to compute the marginal rate of substitution for the following utility functions. a. 1.:(c1, 02} = lnfcl) + ,8 - ln{c2 ) , in which ,3 E {0,1} is an exogenous constant parameter (01 it'llJ] 1+(Cz '3')153 '1 J4 h. tr{cl,c2) : , in which 9! 122-11}, 0'1 :50, and 0'2 '90 are exogenous constant parameters 1..- c. More?) 2 [def + (l t}:}c] p , in which a: E (0,1) and p E (40,1) are exogenous constant parameters 10" 1 {31. national) 2A '51 + C2 l , in which A 2:- 0 and 0' 2':- 0 are exogenous constant parameters o