<Lecture 10> Review: Study Questions ** Suppose that Mr. X has the following utility function: U(F, C) = F 1/2 C 1/2 where F is his consumption of food, with price P F , and C is his consumption of clothing, with P C . a . Derive the marginal utilities for F and C (MU F and MU C ). b . Derive the marginal rate of substitution of F for C (MRS FC ) when F = 1 and C = 3. c . Derive the MRS when F = 3 and C = 1. d . Is the MRS increasing, decreasing, or not changed as we move to the right along the indifference curve? ** Suppose that the income is $100. e . Write the budget constraint. f . Write the Lagrangian Function. g . Derive the first-order conditions. h . Derive the demand functions for F and C. ** Suppose that both P F and P C are $10. i . Calculate the demand quantities for F and C. (F and C) j . Calculate the slope of the demand curve for F. k . Determine the price elasticity of demand for F. l
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