Chapter 7.4, Problem 2MP

Matched Problem 2 The Cobb-Douglas production function for a new product is given by

     $N(x,y)=20x^{0.5}{y}^{0.5}$

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.

1. (A) If $300,000 has been budgeted for the production of this product, how should that amount be allocated in order to maximize production? What is the maximum production?
2. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $40,000 is budgeted for production.