Let x and y denote the amount of goods x and y. The utility is a function of x and y. For each utility function, find the individual demand function.
U = x + xy
*I know how to set up this problem, Can you please show me how to do the correct algebra and simplifying.
A) Let utility over 2 goods be defined as U(x,y)=x+xy+y. Find the MRS by implicitly solving for y (hint: set U=k) and calculate -dy/dx. B) Now find the MRS by using MRS =Ux/Uy.
A consumer has the utility function over goods X and Y, U(X; Y) = X1/3Y1/2 Let the price of good x be given by Px, let the price of good y be given by Py, and let income be given by I. Derive the consumer’s generalized demand function for good X. Solve for the Marshallian Demand for X and Y using Px, and Py (there are no numbers—use the notation). c. Is good Y normal or inferior? Explain precisely.
5. Douglas consumes two goods, x and y. His utility function is u(x) = Vx+y Let the price of good x be $2 and the price of good y be $2. Furthermore, assume that Douglas has $420.00 to spend on these two goods. Find the demand for good x and y. Now suppose that the price of good x decreases to $1.00. What is the income effect and substitution effect of this price change on the demand for x?
Ex. 1: Imagine there are two goods, X and Y. The utility function is: U = XY. The price of X is $2 and the price of Y is $4. The budget is $20. What is the optimal quantity of X and Y to consume? Ex. 2: Imagine there are two goods: books and coffees. Your utility function is U = BC, where B is the number of books you consume and C is the number of coffees you consume....
Find the demand curves for U(x,z) if the utility function is a.) U(x,z)=(x0.5+z0.5)2 b.) U(x,z)= 10x0.5+z Please show all algebra work, the algebra is confusing me as I work through these two problems!! :)
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , available in arbitrary non-negative quantities (so the the consumption set is R 4 +). A typical consumption bundle is therefore a vector (q, r, x, y), where q ≥ 0 is the quantity of good Q, r ≥ 0 is the quantity of good R, x ≥ 0 is the quantity of good X, and y ≥ 0 is the quantity of...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
Suppose the following equations represent an individual’s utility maximization problem: U(X,Y) = X0.5 + Y0.5 And the budget constraint is: I = PxX + PyY (a) Set up the individual’s maximization problem using the Lagrange technique. (b) Find the individual’s demand function for X and Y (Derive from first order condition). (c) Find the indirect utility function. (d) Find the expenditure function. (e) Find the share of X and Y on expenditure. (f) Find the marginal utility of income.
ECON 2023 Spring 2019: Homework #1 Let the utility derived from goods X and Y be as follows for a rational individual Unit of Good TU X TU Y 8 utils 5.5 utils 15 utils 10.5 utils 21 utils 15 utils 26 utils 19 utils 30 utils 22.5 utils 33 utils 25.5 utils З5 utils 28 utils 36 utils 30 utils 36 ubils 31.5 utils 1. Wh 2. What is the functional form of the utility function in a two-commodity...
A consumer of two goods (X and Y) has the following utility function: U(x,y)=xy-ay^2, whre x>=0 and y>=0 and a>0 is a parameter. (a) Are there bundles for which one of the goods is actually a "bad" (in the sense that consuming more of it reduces utility)? (b) Find the MRS.