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# Answer to Question #112778 in Microeconomics for Isabelle miyanda

Question #112778
A firm has the following function Q = 2(xy)^0.5 where x is maize and Y is rice. The cost of maize is k10 and the cost of rice is k40 the firm has a budget of k80 to spend on two goods.
i). Formulate the firms optimization problem
ii). Compute the optimal input combination of x and y
iii). What level of output is associated with the optimal input combination
iv). What is the impact of a k1 increase in the budget
1
2020-04-30T09:59:11-0400

Solution:

i)

"Q=2\\times(xy)^{0.5}"

"P_x=10, P_y=40, I=80"

"P_xQ_x+P_yQ_y=I"

"Q_x=x, Q_y=y"

ii)

"10x+40y=80"

"\\frac{\\partial Q}{\\partial x}=2y^{0,5}x^{-0.5}"

"\\frac {\\partial Q}{\\partial y}=2x^{0.5}y^{-0.5}"

"\\frac {\\frac {\\partial Q}{\\partial x}}{P_x}=\\frac {\\frac{\\partial Q}{\\partial y}}{P_y}"

"\\frac {2 y^{0.5}}{10 x^{0.5}}= \\frac {2 x^{0.5}}{40 y^{0.5}}"

"x=4, y=1"

iii)

"Q=2(4\\times 1)^{0.5}=4"

iv)

An increase in budget for k1 will lead to a decrease in budget for k2

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