2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some...
QUESTION; Given Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is MUx = 4Y; the marginal utility of Y is MUY = 4X. 1) Suppose Y = 3. Calculate Biwei’s utility for X = 2, 3, 10, and 11. For a given level of Y, does good X display diminishing marginal utility? 2) Suppose X = 3. Calculate Biwei’s utility for Y =...
4. consider the following utility functions a) for each of these utility function what is the equation of an indifference curve ? c) for each utility function show weather the function exhibits the diminishing rate of substitution property d) do the above utility function represent the same preference ordering? why or why not? c) Suppose the price of beer doubles, but the price of pizza and Tom's income stay the same. How much beer is Tom consuming as a percentage...
Question 1 For the following utility functions (3 pts each for a, b, and c): • Find the marginal utility of each good at the point (5, 5) and at the point (5, 15) • Determine whether the marginal utility decreases as consumption of each good increases (i.e., does the utility function exhibit diminishing marginal utility in each good?) • Find the marginal rate of substitution at the point (5, 5) and at the point (5, 15) • Discuss how...
2. Say, instead, that an individual's preferences for consumption are expressed according to: Utility - U(C)Ca, where C is consumption. Is the value of a positive or negative? Base your answer on your intuition about individuals' preferences and knowledge of algebra (helpful to use a graph). a. b. What is the function for the individual's marginal utility? Note: this is the derivative of the utility function with respect to C. c. Is marginal utility positive for all values of C?
Find all the first and second-partial derivatives for the utility function, U -50x 5y 0.2 (a) Give a verbal description of each derivative. (b) Are the marginal functions increasing or decreasing. Use the derivatives to justify your answer b. Given the function Q- Al'KB, explain the terms: constant returns to scale; increasing returns to scale; decreasing returns to scale. Show that the production function, Q -100L0.3K0.5, exhibits decreasing returns to scale and diminishing returns to labour Show that the production...
Suppose a person has a utility function given by U = [xρ + yρ]1/ρ where r is a number between −∞ and 1. This is called a constant elasticity of substitution (CES) utility function. You will encounter CES functions in Chapter 6, where the concept of elasticity of substitution will be explained. The marginal utilities for this utility function are given by MUx=[xρ+yρ]1ρ−1xρ−1 MUy=[xρ+yρ]1ρ−1yρ−1 Does this utility function exhibit the property of diminishing MRSx,y?
3. Consider the following utility function, u(x1;x2)=min[xa1; bxa2]; 00 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods? (b) [15 points] Derive the Hicksian demand functions. Does the Hicksian demand increase with price? 3. Consider the following utility function, (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two...
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? consumption goods normal goods? (b) [ 15 points Derive the Hicksian demand functions. Does the icksian demand increase with price?
Suppose that a consumer’s utility function is U(x,y)=xy+10y. the marginal utilities for this utility function are MUx=y and MUy=x+10. The price of x is Px and the price of y is Py, with both prices positive. The consumer has income I. (this problem shows that an optimal consumption choice need not be interior, and may be at a corner point.) Assume first that we are at an interior optimum. Show that the demand schedule for x can be written as...
Consider the utility function u (c, o) = oc (o = leisure; c = consumption), determine the optimal amount of consumption and leisure if the consumer can work at most 24 hours, the hourly wage is 5 and the price of each unit of consumption is 2. There is no initial income endowment.