2. A firm\'s production function is given by Q(x,y) = 500x0. 6y04 where x and y
ID: 3148675 • Letter: 2
Question
2. A firm's production function is given by Q(x,y) = 500x0. 6y04 where x and y are the number of units of labor and capital, respectively. Labor costs $80 per unit and capital costs $200 per unit and the firm has $100,000 to invest. NOTE: x 0 and y0 a.) Use the method of Lagrange Multipliers to find the amounts of labor and capital that maximize production. What is the maximum production in this case? b.) Suppose the firm can increase their investment to $100,001. Using the Lagrange Multiplier a, determine the impact this change will have on the value of the maximum production
Explanation / Answer
Q = 500 x^0.6 * y^0.4
x =labour
y = capital
80x+ 200y < 100000
maximum at x = 750 , y = 200
Q = 221013
b) x = 750.007
y = 200.002
Q = 221016
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.