![Make x the subject of y -In (3 + e*) x=(y-In 3)/ 2 X(ey 3)/2 x-y/ (2 In 3) x [In (3 - ey)]/ 2 x=ln (Vey-3) which of the following could represent a function, 1f (x,y), with first-order partial derivatives af/ax Xy (xy +3) xy 3x-y-6 x (xy + 3) on se the reduced form of a macroeconomic model is Y- (b +I* + G* - aT*)/ (1- a - at) where t is the marginal rate of taxation. Find an expression for the marginal rate of taxation multiplier. [a (aT* - b - I* - G*)]/ (1-a - at) [a (aT* -b - I* - G*)]/ (1-a - at) [a (aT* +b - I* - G*)]/(1 -a - at)](http://img.homeworklib.com/questions/c566dda0-471b-11ea-8bdf-a140da65d0e0.png?x-oss-process=image/resize,w_560)
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Make x the subject of y -In (3 + e*) x=(y-In 3)/ 2 X(ey 3)/2 x-y/...
Solve the following Utility Maximization Problem for x* and y* that Max U(x,y)= ln(x) subject to...
Solve the following Utility Maximization Problem for x* and y* that Max U(x,y)= ln(x) subject to Pxx + pyy = I ----.-.(2) where In denotes the natural logarithm (base e) and x and y>0. a) (25 points) by Substitution and show that your values of x* and y* max U (x*,y*). Problem 1. b) (20 points) by the Lagrange Multiplier Method
1. Which of the following could represent a function, f (x,y), with first-order partial derivatives ∂ƒ/...
1. Which of the following could represent a function, f (x,y), with first-order partial derivatives ∂ƒ/ ∂x = 3xy (xy + 2) ∂ƒ/ ∂y = x2 (2xy + 3) A. xy (x2y + 3) B. x3y2 + 3x2 – y – 6 C. x2 (xy2 + 3) D. none of these E. x3y2 + 2x2y3 + 1 2. It the consumption function is C = 0.02Y2 + 0.1Y +25. Find the value of Y when MPS = 0.38. 3. State...
(1 point) If f(x, y) = x*ey, compute the partial derivatives: fær(1, 3) = fyy(1, 3)...
(1 point) If f(x, y) = x*ey, compute the partial derivatives: fær(1, 3) = fyy(1, 3) = fry(1,3) = fyz (1, 3) =
The goal is to find the minumum and maximum of the function f(x,y)= (1/x)-(1/y) subject to...
The goal is to find the minumum and maximum of the function
f(x,y)= (1/x)-(1/y) subject to the constraint
g(x,y)=(1/x^2)+(3/y^2)=1
10. (7 points) The goal of this problem is to find the maximum and minimum values of the function (x) subject to the constraint g(x,y) = +3=1. a) Set up a Lagrange multiplier system modeling this problem. (b) Solve the system you set up in part (a). (c) Identify the extrema.
A firm’s demand function is p=60-0.5Q If fixed cost are 10 and variable cost are Q+3...
A firm’s demand function is p=60-0.5Q If fixed cost are 10 and variable cost are Q+3 per unit, find the maximum profit. Q2. Which of the following could represent a function, f(x,y), with first-order partial derivatives af/ax = 3xy(xy+2) af/ay=x^2(2xy+3) Q3. Find the value of dy/dx at the point (-2,1) for the function which is defined implicitly by x^2 - x/y =6 Q4. Find the value of the marginal rate of technical substitution for the production function Q=300 (K^2/3 )(L^1/2)...
An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten...
An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten dollars (I = $10) The price of item x is $1. The price of item y is $1. Maximize this consumer’s utility subject to a budget constraint using the Lagrange Multiplier method. At what point does the marginal rate of substitution equal the price ratio?
Homework #1 Name: 1) What are the differences and similarities between a recession and a depression?...
Homework #1 Name: 1) What are the differences and similarities between a recession and a depression? 2) What is the economic definition of unemployment? 3) Define inflation. What is one potential macroeconomic consequence of inflation? 4) Take the partial derivatives of the following function with respect to x. f(x)-3x3+4xy -xy+3x-1 5) Take the partial derivatives of the following function with respect to y f(y)-3x3 +4x2y -xy +3x-1
3. In the following, consider z as a function of x and y, i.e., z =...
3. In the following, consider z as a function of x and y, i.e., z = z(x, y) and use az az implicit differentiation to find the partial derivatives and ax ay (a) x2 + y2 + z2 = 3xyz (b) yz = ln(x + z)
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the...
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
Solve the following Utility Maximization Problem for x* and y* that Max U(x,y)= ln(x) subject to Pxx + pyy = I ----.-.(2) where In denotes the natural logarithm (base e) and x and y>0. a) (25 points) by Substitution and show that your values of x* and y* max U (x*,y*). Problem 1. b) (20 points) by the Lagrange Multiplier Method
(1 point) If f(x, y) = x*ey, compute the partial derivatives: fær(1, 3) = fyy(1, 3) = fry(1,3) = fyz (1, 3) =
The goal is to find the minumum and maximum of the function
f(x,y)= (1/x)-(1/y) subject to the constraint
g(x,y)=(1/x^2)+(3/y^2)=1
10. (7 points) The goal of this problem is to find the maximum and minimum values of the function (x) subject to the constraint g(x,y) = +3=1. a) Set up a Lagrange multiplier system modeling this problem. (b) Solve the system you set up in part (a). (c) Identify the extrema.
Homework #1 Name: 1) What are the differences and similarities between a recession and a depression? 2) What is the economic definition of unemployment? 3) Define inflation. What is one potential macroeconomic consequence of inflation? 4) Take the partial derivatives of the following function with respect to x. f(x)-3x3+4xy -xy+3x-1 5) Take the partial derivatives of the following function with respect to y f(y)-3x3 +4x2y -xy +3x-1
3. In the following, consider z as a function of x and y, i.e., z = z(x, y) and use az az implicit differentiation to find the partial derivatives and ax ay (a) x2 + y2 + z2 = 3xyz (b) yz = ln(x + z)
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
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