For all the utility functions (CES, Cobb-Douglas, quasi-linear, linear, Stone-Geary and Leontief) in the attached document, formally derive the Marshallian demand functions and the related expenditure functions.
For all the utility functions (CES, Cobb-Douglas, quasi-linear, linear, Stone-Geary and Leontief) in the attached document,...
8. Explain how three of the most common production functions (Linear, Cobb Douglas and Leontief) are particular cases of the Constant Elasticity of Substitution production function.
4. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1x2) = xx-. a) Show that marginal utility is decreasing in X and X2. What is the interpretation of this property? b) Calculate the marginal rate of substitution c) Assuming an interior solution, solve for the Marshallian demand functions.
1 Elasticity 2. What is special about the elasticity of a Cobb-Douglas utility function? 3. Assume a linear demand curve. Why is the consumer's expenditure maximized where ε = -1?
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What restrictions does a Cobb-Douglas lity function (preferences) impose on demand functions? Explain your answer. marks) 1/4 Maximize u = x;"/4x2 4x, + 2x, = 100 Subject to - Use the information in above to derive the consumer's indirect utility anction (value function) and then prove Roy's identity (10 marks)
Roger's utility function is Cobb-Douglas, U = 80.67 20.33, his income is Y, the price of B is PB, and the price of Z is pz. Derive his demand curves. Roger's demand functions are B= and Z= . (Enter any numbers rounded to two decimal places. Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ character.)
All you need to worry about is solving for the Marshallian
Demand Functions for both questions. I'm okay w/ deriving MDFs for
Cobb-Douglas functions and Leontief functions, but #3 (Quasilinear)
and #4 (Linear) I struggle with. Explain the steps if possible
3. Lady Marchmain has the following utility function over bread (b) and housing (h): Let Y denote Lady Marchmain's total income; let Po denote the price of bread; and let Ph denote the price of housing. a. Solve for...
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
Please answer the following question. (30 pts possible) 1 Consider the following (Cobb-Douglas) utility function: And budget constraint: M2 PX+PY 1. *Treat P, Py, M, a, and B as positive constants. Note, a +B Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) Show that the...
4. Suppose you have the following Cobb-Douglas Utility Function: And $200 to spend. a. Use the method of Lagrangian Multipliers, to maximize this consumer's utility and derive demand equations for both goods. Sketch their respective demand curves. Show all work. (5 pts) b. If Px = Py = $1, how much utility will the consumer enjoy? Show work/explain. (2.5 pts) c. Does this allocation satisfy the rule of equal marginal utility per dollar spent? Explain/show work. (2.5 pts)
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....