Question

lomework (Ch 14) A U.S. export-import shipping company operates a general cargo carrier service between New York and several western European ports. It hauls two major categories of freight: manufactured items (Q.) and semimanufactured raw materials (Q:). The demand functions for these two classes of goods are: P = 200 - Q. P=80-Q, where tons of freight moved. The total cost function for the United States is 7C - 20 + 4(Q. +Q) What is the firm's total profit function? 1960. - Q.? + 76Q: - Q 1960.-Q.? +76Q-Q;? –20 1990. -0,' +600, -0,1 -20 2009.-Q.? +800, -0,2-20 The profit maximizing levels of price and output for manufactured items are S per ton and tons, respectively. The profit maximizing levels of price and output for semimanufactured raw materials are SIM per ton and tons, respectively,

Answer 1

Total Revenue is given by

TR=P₁*Q₁+P₂*Q₂

TR=(200-Q₁)*Q₁+(80-Q₂)*Q₂=200Q₁-Q₁²+80Q₂-Q₂²

TC=30+4(Q₁+Q₂)=20+4Q₁+4Q₂

Profit=TR-TC

Profit=(200Q₁-Q₁²+80Q₂-Q₂²)-(20+4Q₁+4Q₂)

Profit=196Q₁-Q₁²+76Q₂-Q₂²-20

Correct option is

196Q₁-Q₁²+76Q₂-Q₂²-20

Let us consider the case of manufactured items first

d(Profit)/dQ₁=196-2Q₁

Put d(Profit)/dQ₁=0 for profit maximization

196-2Q₁=0

Q₁=196/2=98 tons (optimal output for manufactured items)

P₁=200-Q₁=200-98=$102   (optimal price for manufactured items)

Let us consider the case of semi manufactured raw material now

d(Profit)/dQ₂=76-2Q₂

Put d(Profit)/dQ₂=0 for profit maximization

76-2Q₂=0

Q₂=76/2=38 tons (optimal output for semi manufactured raw material)

P₁=80-Q₂=80-38=$42 (optimal price for semi manufactured raw material)