Adam's Utility at Optimal Consumption Bundle Given Adam's utility function U = 4x0.8y 0.2 And the optimal consumption bundle found previously (X= 40, Y = 30), substitute these values into the utility function. U = 4 \times 400.8 \times 300.2 U = 4 \times 19.127 \times 300.2 U = 76.5 \times 1.97 U 151 Adam's utility at his optimal consumption bundle is 151. C. The Lagrange multiplier at the optimal consumption bundle can be interpreted as the marginal utility of income, or how much additional utility Adam would gain from an additional unit of currency. From the Lagrange multiplier method, dL = 3.2X-0.20.2 451 = 0 dt = 0.8x087-08-151 = 0 Using equation 1, 3.2 \times 40-0.2 \times 300.2= 452 45m= 3.2.40-0.2 300.2 452 = 32= 0.067 d. Budget Constraint Line PX. X + PY. Y = B With PX = £45, PY= £15, and B = £2,250, this becomes 45X + 15Y = 2,250. Set Y to 0 in the budget equation, 45X = 2250, X = 50. The X-intercept is at (50, 0). Set X to 0, 15Y = 2250, Y= 150. The Y-intercept is at (0, 150). Explanation: The slope of the budget line is Py 45= 15 -3. This means for every unit increase in X, Y decreases by 3 units. The Indifference Curve is a smooth, convex curve to the origin and will pass through the point (40, 30), which is the optimal consumption bundle. (DRAW MEA A DIAGRAM) .
Adam's Utility at Optimal Consumption Bundle Given Adam's utility function U = 4x0.8y 0.2 And the optimal consumption bundle found previously (X= 40, Y = 30), substitute these values into the utility function. U = 4 \times 400.8 \times 300.2 U = 4 \times 19.127 \times 300.2 U = 76.5 \times 1.97 U 151 Adam's utility at his optimal consumption bundle is 151. C. The Lagrange multiplier at the optimal consumption bundle can be interpreted as the marginal utility of income, or how much additional utility Adam would gain from an additional unit of currency. From the Lagrange multiplier method, dL = 3.2X-0.20.2 451 = 0 dt = 0.8x087-08-151 = 0 Using equation 1, 3.2 \times 40-0.2 \times 300.2= 452 45m= 3.2.40-0.2 300.2 452 = 32= 0.067 d. Budget Constraint Line PX. X + PY. Y = B With PX = £45, PY= £15, and B = £2,250, this becomes 45X + 15Y = 2,250. Set Y to 0 in the budget equation, 45X = 2250, X = 50. The X-intercept is at (50, 0). Set X to 0, 15Y = 2250, Y= 150. The Y-intercept is at (0, 150). Explanation: The slope of the budget line is Py 45= 15 -3. This means for every unit increase in X, Y decreases by 3 units. The Indifference Curve is a smooth, convex curve to the origin and will pass through the point (40, 30), which is the optimal consumption bundle. (DRAW MEA A DIAGRAM) .
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Adam's Utility at Optimal Consumption Bundle Given Adam's utility function U = 4x0.8y 0.2 And the optimal
consumption bundle found previously (X= 40, Y = 30), substitute these values into the utility function. U = 4 \times
400.8 \times 300.2 U = 4 \times 19.127 \times 300.2 U = 76.5 \times 1.97 U = 151 Adam's utility at his optimal
consumption bundle is 151. C. The Lagrange multiplier at the optimal consumption bundle can be interpreted as the
marginal utility of income, or how much additional utility Adam would gain from an additional unit of currency. From the
Lagrange multiplier method, dL = 3.2X-0.20.2 - 451 = 0 dt = 0.8x087-08-151 = 0 Using equation 1, 3.2 \times
40-0.2 \times 300.2= 452 45= 3.2.40-0.2 300.2 452 = 32 = 0.067 d. Budget Constraint Line PX. X + PY. Y
= B With PX = £45, PY = £15, and B = £2,250, this becomes 45X + 15Y= 2,250. Set Y to 0 in the budget equation,
45X = 2250, X = 50. The X-intercept is at (50, 0). Set X to 0, 15Y = 2250, Y = 150. The Y-intercept is at (0, 150).
Explanation: The slope of the budget line is Py 45= 15 = -3. This means for every unit increase in X, Y decreases
by 3 units. The Indifference Curve is a smooth, convex curve to the origin and will pass through the point (40, 30), which
is the optimal consumption bundle. (DRAW ME A A DIAGRAM)
-
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