TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON-4000 TOPICS IN ADVANCED MICROECONOMIC THEORY ASSIGNMENT 1 DUE: FEBRUARY 12, 2024 Answer all questions. Each is equally weighted. Question 1: Consider a consumer whose utility function is given by U(x₁, x₂) = x₁x2, where x and y represent quantities of consumption of two consumer goods. and x2. 3/41/4 (a) Derive and interpret this consumer's Marshallian demand functions for X1 (b) Derive and interpret this consumer's indirect utility function. (c) Derive and interpret this consumer's Hicksian demand functions for x₁ and x2. (d) Derive and interpret this consumer's expenditure function. (e) Suppose the consumer's income is $1000 and the prices of x, and x2 are both $5. How should the consumer maximize her utility? What is her maximum level of utility? (d) Now suppose the price of x, rises to $10. The price of x2 remains at $5. (i) Derive, explain, and illustrate the income and substitution effects of this price change on the consumption of x₁. (ii) Derive, explain, and interpret the income and substitution effects of this price change on the consumption of x2. (iii) What are the effects of this price change on the consumer's maximum utility? +

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