Bus Econ 9.4.31 EQuestion Help The Cobb-Douglas production function for a partic

Question

Bus Econ 9.4.31 EQuestion Help The Cobb-Douglas production function for a particular product is N(xy)-80x y3, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40 and each unit of capital costs $120 If $800,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production. Production will be maximized when using units of labor and units of capital.

Explanation / Answer

We have given

40x+120y=800000

x+ 3y =20000

x = 20000 -3y

Thus we have function

N(x) = 80( 20000 -3y)^(0.7)y^(0.3)

Now using TI83, function has extrema at y= 2000

Hence

x =20000 -3*2000 = 14000

Hence

14000 units of labor and 2000 units of capital

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