1. 2. Suppose a firm has a cost function: TC = 4x2 + 10y2. The production manager want to know the quantities of each product that will minimize the total cost if the total output of x & y must equal 800.
a. Solve this problem for the manger using the Lagrangian method.
b. How would this manager use the resulting Lagrangian multiplier in this case?
2.
1. Suppose a firm sells two products labeled: x & y. The total revenue function for these products is: TR = 36x - 3x2 + 40y - 5y2. And the total cost function is: TC = x2 + 2xy + 3y2. Find:
a. The optimal levels of x & y this form should produce to maximize profits.
b. Be sure to check and show the second order conditions confirming your results.
c. What are the prices of both goods x & y at the optimal levels?
3.
3. The supply function for a particular kind of cheese is: Qs = 100 + 3P where Qs is the quantity supplied of this cheese in millions of pound per year, and P is the price of this cheese in dollars per pound. If the demand function is: Qd = 106 million pound of cheese per year and if the government imposes a price floor of $1 per pound:
a. Will there be excess supply or excess demand for this cheese? How big will it be?
b. What if the government sets a price floor of $3 per pound? Will there be excess demand or supply? How big will it be?