The equation $ y = x_1^{1/2} x_2^{1/4} $ is given with $ x_2 $ fixed at 81. The cost of input $ x_1 $ is $ w_1 = 5 $, the cost of input $ x_2 $ is $ w_2 = 3 $, and $ p = 10 $.The task is to determine which expression represents the correct calculation of profits.Options:1. $ \pi = x_1^{1/2} x_2^{1/4} - x_1 x_2 $2. $ \pi = 10x_1^{1/2} 81^{1/4} - 5x_1 - 3(81) = 30x_1^{1/2} - 5x_1 - 243 $3. $ \pi = x_1^{1/2} 81^{1/4} - 5x_1 - 3(81) = 3x_1^{1/2} - 5x_1 - 243 $4. $ \pi = x_1^{1/2} 81^{1/4} - x_1 - 81 = 3x_1^{1/2} - x_1 - 81 $The question asks to identify the correct expression for profits, given the equations and parameters stated.

x2 is fixed. Put the value of x2 into production function. Profit = revenue - cost Revenue = PY…

y = x1% x2 and x 2 is fixed at 81; the cost of input x1 is w 1=5; the cost of input x2 is w 2 = 3; p =10 Which expression is the correct expression of profits? T = X1 2 x 2 4 - x 1 x 2 TT = 10x1½ 81% - 5x1 -3(81) = 30x12 . 5x1 - 243 TT = xq% 814 - 5x1 -3(81) = 3x1½ - 5x1 - 243 п-х181- х1- 81 %3D 3х1 -х1-81

y = x1% x2 and x 2 is fixed at 81; the cost of input x1 is w 1=5; the cost of input x2 is w 2 = 3; p =10 Which expression is the correct expression of profits? T = X1 2 x 2 4 - x 1 x 2 TT = 10x1½ 81% - 5x1 -3(81) = 30x12 . 5x1 - 243 TT = xq% 814 - 5x1 -3(81) = 3x1½ - 5x1 - 243 п-х181- х1- 81 %3D 3х1 -х1-81

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

The equation $ y = x_1^{1/2} x_2^{1/4} $ is given with $ x_2 $ fixed at 81. The cost of input $ x_1 $ is $ w_1 = 5 $, the cost of input $ x_2 $ is $ w_2 = 3 $, and $ p = 10 $.

The task is to determine which expression represents the correct calculation of profits.

Options:

1. $ \pi = x_1^{1/2} x_2^{1/4} - x_1 x_2 $

2. $ \pi = 10x_1^{1/2} 81^{1/4} - 5x_1 - 3(81) = 30x_1^{1/2} - 5x_1 - 243 $

3. $ \pi = x_1^{1/2} 81^{1/4} - 5x_1 - 3(81) = 3x_1^{1/2} - 5x_1 - 243 $

4. $ \pi = x_1^{1/2} 81^{1/4} - x_1 - 81 = 3x_1^{1/2} - x_1 - 81 $

The question asks to identify the correct expression for profits, given the equations and parameters stated.

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