Question

In: Economics

If a firm’s production is f(x1,x2) = 2x11/2 x21/4. If the price of factor 1 is...

If a firm’s production is f(x₁,x₂) = 2x₁^1/2 x₂^1/4. If the price of factor 1 is $5 and the price of factor 2 is $10, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? Please show all work clearly.

Expert Solution

The firms production function is given by,

Differentiating the Production function wrt x1, we get

Similarly by differentiating Q wrt x2 we get,

The firm will be optimally utilizing it's resources at the point where the equi marginal criterion will be satisfied.

Plug in the given values we get

From above we can see that 1 unit of factor x1 must be equal to 4 times the unit of x2.

Rahul Sunny answered 2 years ago

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