American Export Import Shipping Company Operates A General C

American Export Import Shipping Company Operates A General Cargo Ca

American 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 and semi-manufactured raw materials. The demand functions for these two classes of goods are P1 = 100 − 2Q1 and P2 = 80 − Q2, where Q1 and Q2 are tons of freight moved. The total cost function for American is TC = 20 + 4(Q1 + Q2).

What are the profit-maximizing levels of price and output for the two freight categories?

At these levels of output, calculate the marginal revenue in each market.

What are American’s total profits if it is effectively able to charge different prices in the two markets?

Sample Paper For Above instruction

Introduction

The shipping industry plays a crucial role in facilitating international trade by transporting goods across different regions. American Export-Import Shipping Company operates a general cargo service between New York and Western European ports, catering to two primary freight categories: manufactured items and semi-manufactured raw materials. The company's revenue optimization involves determining the profit-maximizing price and quantity for each freight type, considering demand functions and cost structures. This paper analyzes the profit maximization strategies for the company, calculates the corresponding marginal revenues, and estimates total profits under the assumption of price discrimination.

Demand Functions and Cost Structure

The demand functions for the two freight categories are given by P1 = 100 − 2Q1 for manufactured items and P2 = 80 − Q2 for semi-manufactured raw materials, where P represents price per ton and Q the quantity in tons. The total cost function is TC = 20 + 4(Q1 + Q2), reflecting fixed costs and variable costs proportional to total freight transported. The company seeks to determine the optimal quantity and price for each market that maximizes profit, defined as total revenue minus total costs.

Profit Maximization Analysis

To identify the profit-maximizing output, the company must derive marginal revenue (MR) functions for each market, set them equal to marginal cost (MC), and solve for Q1 and Q2.

Marginal Revenue in Market 1:

Given P1 = 100 - 2Q1, total revenue (TR1) = P1 × Q1 = (100 - 2Q1)Q1 = 100Q1 - 2Q1^2.

Derivative of TR1 with respect to Q1 yields MR1 = d(TR1)/dQ1 = 100 - 4Q1.

Marginal Revenue in Market 2:

Given P2 = 80 - Q2, TR2 = (80 - Q2)Q2 = 80Q2 - Q2^2.

MR2 = d(TR2)/dQ2 = 80 - 2Q2.

Marginal Cost (MC):

Since total cost TC = 20 + 4(Q1 + Q2), marginal cost for each additional ton is constant at MC = d(TC)/dQ = 4.

Setting MR equal to MC:

For Q1: 100 - 4Q1 = 4 → 100 - 4Q1 = 4 → 4Q1 = 96 → Q1* = 24.

Corresponding price: P1* = 100 - 2(24) = 100 - 48 = 52.

For Q2: 80 - 2Q2 = 4 → 80 - 2Q2 = 4 → 2Q2 = 76 → Q2* = 38.

Corresponding price: P2* = 80 - 38 = 42.

Calculation of Marginal Revenue

The MR functions at optimal quantities are:

MR1 = 100 - 4(24) = 100 - 96 = 4

MR2 = 80 - 2(38) = 80 - 76 = 4

The fact that both marginal revenues equal the constant marginal cost confirms the correctness of the profit-maximizing output levels.

Total Profit Calculation

Total revenue (TR) in each market:

TR1 = P1 × Q1 = 52 × 24 = 1248

TR2 = P2 × Q2 = 42 × 38 = 1596

Total cost: TC = 20 + 4(24 + 38) = 20 + 4(62) = 20 + 248 = 268

Total profit (π):

π = (TR1 + TR2) - TC = (1248 + 1596) - 268 = 2844 - 268 = 2576

Conclusion:

American Export-Import Shipping Company maximizes its profit by transporting 24 tons of manufactured items at a price of $52 per ton and 38 tons of raw materials at a price of $42 per ton. Under these optimal levels, the company’s total profit is $2,576, with marginal revenues in each market equaling the marginal cost, aligning with economic theory on profit maximization.

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