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Answer to Question #111562 in Microeconomics for GP

Question #111562
A firm has the following production 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 the two goods.
i. Formulate the firmsâ€™ optimization problem.
ii. Compute the optimal input combination of good 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
2020-04-23T11:53:33-0400

Solution:

"Q=2(xy)^2"

"p_x=10, p_y=40, I=80"

i)

"\\frac{\\frac{\\partial Q}{\\partial x}}{p_x}=\\frac{\\frac{\\partial Q}{\\partial y}}{p_y}"

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

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

ii)

"4y=x"

y=1; x=4.

iii)

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

iv)

An increase in budget x will lead to a decrease in production y.

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