Given f(x,y) = 2x2 - 5xy + 5y2, and Px= 7, Py= 6 and income, I = 169. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required)
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Given f(x,y) = 2x2 - 5xy + 5y2,
and Px= 7, Py= 6 and income, I = 169.
Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y.
(a) What is the equilibrium value of x? (Give your answer to two decimal places, if required)
(b) What is the equilibrium value of y? (Give your answer to two decimal places, if required)
(c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required)
(d) Based on the value of the Bordered Hessian, comment whether the obejective function is maximised or minimised.
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- Given f(x,y) = 2x2 - 6xy + 9y2, and Px= 7, Py= 5 and income, I = 175. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) unanswered d. Based on the value of the Bordered Hessian, comment whether the objective function is maximized or minimized. Answer in one word.In the below figure, a consumer is initially in equilibrium at point C. The consumer’s income is $250, and the budget line through point C is given by $250 = $50X + $125Y. When the consumer is given a $100 gift certificate that is good only at store X, she moves to a new equilibrium at point D. "The horizontal axis is labeled Product X. The vertical axis is labeled Product Y. A line begins at point A on the vertical axis goes down to the right and ends at point E on the horizontal axis. A second line parallel to the first one begins at point B in the first quadrant close to point A, goes down to the right and ends at point F on the horizontal axis. A horizontal line connects point A and B. An upward-facing curve labeled l-subscript 1 begins at the top left of the quadrant along the vertical axis, goes down to the right in decreasing steepness, intersects the horizontal line [AB], meets the first line at point C then continues with increasing to the right and above the line to exit…Suppose the government implements an income support program with the intention of making sure residents are able to purchase sufficient food. The government pays a cash benefit to all individuals with incomes less than $1000 according the following formula: cash benefit (CB) = $200 – 0.2*(earned income(I)) Households spend all of their income on food (F) and other goods (X). The price of food and other goods are normalized to 1. A households budget constraint is F + X = CB + I Households have the following preferences: U = 0.25*ln(F) + 0.75*ln(X) Refer to Scenario 3 Suppose a household has earned income of $300 and instead of cash, the government benefit is in the form of food stamps, or vouchers, that must be spent on food. How much does the household spend on food now?
- I need asnwers of a,c,g. Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?Scenario 3 Suppose the government implements an income support program with the intention of making sure residents are able to purchase sufficient food. The government pays a cash benefit to all individuals with incomes less than $1000 according the following formula: cash benefit (CB) = $200 – 0.2*(earned income(I)) Households spend all of their income on food (F) and other goods (X). The price of food and other goods are normalized to 1. A households budget constraint is F + X = CB + I Households have the following preferences: U = 0.25*ln(F) + 0.75*ln(X) Refer to Scenario 3 Suppose instead of cash, the government benefit is in the form of food stamps, or vouchers, that must be spent on food. How much does the household spend on food now?Scenario 3 Suppose the government implements an income support program with the intention of making sure residents are able to purchase sufficient food. The government pays a cash benefit to all individuals with incomes less than $1000 according the following formula: cash benefit (CB) = $200 – 0.2*(earned income(I)) Households spend all of their income on food (F) and other goods (X). The price of food and other goods are normalized to 1. A households budget constraint is F + X = CB + I Households have the following preferences: U = 0.25*ln(F) + 0.75*ln(X) Refer to Scenario 3 Suppose a household has earned income of $300. How much does this household receive in benefits? and how much does the household spend on food?
- In the above figure a consumer is initially at equilibrium at point C. The consumer’s income is $400, and the budget line through point C is given by $400 = 100X + 200Y. When the consumer is given a $100 gift certificate that is good only for product X, she moves to a new equilibrium point at point D. (a) How many units of product X will be purchased at point B? Please explain. (b) How many units of Product X will be purchased at point F? Please explain. (c) Please rank the bundles of goods A, B, C, D, from least preferred to most preferred (from lowest utility or satisfaction to highest utility of satisfaction).I need asnwers of f,g Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?1. Use the Method of Lagrange to solve this problem. To do so, construct the La- grangean function for this problem. Use λ1 as the Lagrange multiplier attached to the period 1 budget constraint and λ2 as the Lagrange multiplier attached to the period 2 budget constraint.
- (In this question we denote income by Y, not by W as in the lecture notes). The following figure shows a two-good consumption space for an agent. The horizontal axis measures good x and the vertical axis measures good y. There are three budget lines shown in the figure. The first budget line has vertical intercept Y/py and horizontal intercept Y/px. The second budget line has vertical intercept Y/p’y<Y/py, and horizontal intercept Y/px. The third budget line has vertical intercept Y/py, and horizontal intercept Y/p’x< Y/px. There are two indifference curves. These are downward sloping thin curves that do not touch. One of this curves intersects the first budget line only at bundle (3,2). The other curve intersects the second budget line only at (4,0.6) and intersects the third budget line only at (1,2.5). Can we conclude that good y is a Giffen good for some market situation? No. Yes.(In this question, differently from our lecture notes, income will be denoted by Y, not W). The following figure shows a two-good consumption space for an agent. The horizontal axis measures good x and the vertical axis measures good y. There are three budget lines shown in the figure. The first budget line has vertical intercept Y/py and horizontal intercept Y/px. The second budget line has vertical intercept Y/p’y<Y/py, and horizontal intercept Y/px. The third budget line has vertical intercept Y/py, and horizontal intercept Y/p’x< Y/px. There are two indifference curves. These are downward sloping thin curves that do not touch. One of this curves intersects the third budget line only at bundle (3,2). The other curve intersects the second budget line only at (4,0.6) and intersects the third budget line only at (1,2.5). Then Qx(px,py,Y), the demand of good x for prices px and py and income Y is: 4 1 2.5 2 3For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x and x2 are p₁ and p₂ respectively and income is m. i) U(x1x2) = ln(x1+ x2) ii) U(x1x2) = (x1+ x2)