MaGeehkaal
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i was given a Cobb-douglas production function Q(K,L)= 40k^0.8L^0.2 where K is the number of units of capital and L the number of units of labour required to produce Q units of the product.

Each unit of capital cost $60 and each unit of labour cost $120 , it is also stated that $1,200,000 is budgeted for production of the product.

how can i find when production will be maximized solving for K and L?
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josh_v
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Its been 2 years since I've done this, so may be wildly incorrect but I believe you do the following:

Create your budget constraint given that you know the cost of capital, labour and the total amount budgeted.

Use this to create your lagrange equation.

Partially differentiate w.r.t K and L.

Equate these two equations and get a value for either K or L. You can then use this to find the value of the other.

Once you have values of K and L, you use this to find Q.
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