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) Let utility over 2 goods be defined as U(x,y)=x+xy+y. Find the MRS by implicitly solving...
For U(x,y) -xy, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x andy For U(x,y)-x2y2, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x and y For U(x,y) = In x + In y, MRS- ,while Ux- and Uyy ▼ . This means that this utility function has MRS, while exhibiting marginal utility in x and...
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.
Calculate the MRS for the following three utility functions: ·U(x,y) = xy . U(x,y) = lnx + lny . U(x, y) = x2y2 Is the result suprising? If yes, try to explain it.
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 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.
2. Jane's utility function defined over two goods and y is U (x, y) = !/2y\/? Her income is M and the prices of the two goods are p, and Py. (e) Determine the substitution and income effects for good when ini- tially M = $12. Pa = $2, Py = $1, and then the price of good rises to $3. (f) Show the effects from the previous part graphically. (g) How many dollars is Jane willing to accept as...
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)
Let the function f be defined by f(x,y)-- уз +4y2-15y + x2-8x . The set A consists of all points (x,y) in the xy-plane that satisfy 0sx s 10, 0sy s10 and x+y 28. Find the global minimum value of f(x,y) over the set A. (Hint: see Let the function f be defined by f(x,y)-- уз +4y2-15y + x2-8x . The set A consists of all points (x,y) in the xy-plane that satisfy 0sx s 10, 0sy s10 and x+y...
3. (ICs for Quasi-Linear Preferences) Consider the utility function: u(x, y) = x1/2 + y. a. Find the expression for the MRS (= – dy/dx). b. Draw one IC making sure its shape reflects your expression for MRS above. c. Given your expression for MRS, draw another IC above the one you just drew, and comment on how the slopes of the ICs compare at a given level of x (e.g., at x = 1).
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...