Assume that the firm’s operation is subject to the following production function and price data: Q=3X+5Y-XY Px= 3 $ Py= 6 $ where X and Y are two variable input factors employed in the production of Q. A. In the unconstrained case, what levels of X and Y will maximize Q? B. It is possible to express the cost function associated with the use of X and Y in the production of Q as TC = 3X + 6Y subject to the firm’s constraint of an operating budget of $25. Use the Lagrange multiplier technique to determine the optimal levels of X and Y. What is the firm’s total output at these levels of input usage? What is the value of Lagrangian multiplier? C. What will happen to the firm’s output from a marginal increase in the operating budget? (Hint: This is another way of asking you to interpret the Lagrangian multiplier you found in B above).
Assume that the firm’s operation is subject to the following production function and price data:
Q=3X+5Y-XY
Px= 3 $
Py= 6 $
where X and Y are two variable input factors employed in the production of Q.
A. In the unconstrained case, what levels of X and Y will maximize Q?
B. It is possible to express the cost function associated with the use of X and Y in the production of Q as TC = 3X + 6Y subject to the firm’s constraint of an operating budget of $25. Use the Lagrange multiplier technique to determine the optimal levels of X and Y. What is the firm’s total output at these levels of input usage? What is the value of Lagrangian multiplier?
C. What will happen to the firm’s output from a marginal increase in the operating budget? (Hint: This is another way of asking you to interpret the Lagrangian multiplier you found in B above).
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