(1) Matilda consumes a composite good (c) and food (s). Her preferences are represented by the utility function u(c,s)= aln s + (1-a)Inc Suppose the price of the composite good and food ae Pc and Ps, respectively; and her budget is B. You are required to do the following: a) Specify Matilda's budget set b) Explain the expenditure on each of the two commodities consumed c) Specify the Lagrangian function d) Derive the Marshallian demand function for each of the two commodities e) How many units of each of the two commodities will be consumed by Matilda if her income is GHS100.00 and alpha=0.4; Pc-GHS1.00; Ps-GHS2.00? f) Derive the indirect utility function and verify the Roy's identity g) Re-specify the Lagrangian function and derive the Hicksian demand function for each of the two commodities h) Derive the expenditure function using the Hicksian demand function i) Using the Shepherd's Lemma, verify the Hicksian demand function (2) Based on the functions derived in question 1, clearly demonstrate how a Marshallian demand function can be derived from the Hicksian demand function