Question;Assignment #3;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?;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?;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?;4.;Given the following Demand and Supply functions for;wheat in the U.S.;Qd = 3.1 ? 0.25P;Qs = 1.3 + 0.5P;Find;a.;Equilibrium price and quantity.;b.;Price elasticity of demand at equilibrium.;c.;If wheat prices increased slightly, would we expect;total revenues to increase or decrease? Explain using the elasticity;coefficient you calculated above.;5.;The B-2 bomber was designed as a stealthy long range;bomber. Two Northrop engineers used mathematical analysis to determine how an aircraft?s;volume should be proportioned between the wing and the fuselage to maximize its;flying range. Taking the derivative of range with respect to volume, they found;that this derivative equaled zero when the total volume was almost all wing.;Hence the result was the flying wing configuration. Thus the engineers;concluded that this configuration would maximize the flight range. However, in;reality, this aircraft exhibits one of the worst flying ranges in the Air Force;inventory. There was a flaw in the engineers? analysis. What was it?;6. Given the;following demand functions;x;= 25 ? 0.5 Px;y;= 30 ? Py;with the combined cost function: c = x2 + 2xy + y2 + 20;Find;The profit maximizing output for;each product.;Price of each product.;Profit.
Paper#54570 | Written in 18-Jul-2015Price : $33