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Calculating optimal price and output combination

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The Steel Supply Corporation is an importer and distributor of Taiwanese-made, 96 piece hand-tool sets (screw drivers, wrenches, and the like). The U.S. Commerce Department recently informed the company that it will be subject to a new 25% tariff on the import cost of fabricated steel. The company is concerned that the tariff will slow its sales growth, given the highly competitive nature of the hand-tool market. Relevant market demand and marginal revenue relations are:

P= $80-$0.0001Q

MR= dTR/dQ =$80-$0.0002Q

The company's marginal cost equals import costs of $32 per unit, plus $8 to cover transportation, insurance, and related selling expenses. In addition to these costs, the company's fixed costs, including a normal rate of return, come to $2,500,000 per year on this product.

A. Calculate the optimal price/output combination and economic profits prior to imposition of the tariff.
B. Calculate the optimal price/output combination and economic profits after imposition of the tariff.
C. Compare your answers to parts A and B. Who pays the economic burden of the import tariff?

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A. Calculate the optimal price/output combination and economic profits prior to imposition of the tariff.

Marginal Cost, MC=Import costs+ other expanses=32+8=$40
MR =$80- $0.0002Q

Firm will maximize its profits by setting its output level such that MR=MC. So, put MR=MC

Q=40/.0002 =200000 units

Total Revenue=TR=P*Q=60*200000=$12,000,000

Fixed cost=$2,500,000
Variable Costs=40*200000=$8,000,000
Total Cost, TC=Fixed Cost+ Variable ...

Solution Summary

Solution describes the steps to calculate optimal price, output and associated profit with and without imposition of tariff.

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A television station is considering the sale of promotional DVDs. It can have the DVDs produced by one of two suppliers. Supplier A will charge the station a set-up fee of $1,200 plus $2 for each DVD; supplier B has the no set-up fee and will charge $4 per DVD. The station estimates its demand for the DVDs to be given by Q = 1,600 - 200P, where P is the price in dollars and Q is the number of DVDs. (The price equation is P = 8 - Q / 200).

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b. Suppose instead that the stations seek to maximize its profits from sales of the DVDs. What price should it charge? How many DVDs should it order from which supplier?

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