Consider a Cobb-Douglas utility function U (X, Y) = Xα Y (1- α), Where X and y are the two goods that a consumer consumes at per unit prices of Px and Py respectively. Assuming the income of the consumer to be ₹M, determine: a. Marshallian demand function for goods X and Y. b. Indirect utility function for such a consumer. c. The maximum utility attained by the consumer where α =1/2, Px =₹ 2, Py = ₹ 8 and M= ₹ 4000. d. Derive Roy’s identity.
Introduction The Cobb-Douglas utility function is one of the most widely used utility functions in microeconomics. It models consumer preferences where two goods are consumed in fixed proportions. This problem involves the derivation of the Marshallian demand, indirect utility, and application of specific values to determine maximum utility. We also derive Roy’s identity, which helps […]