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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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Solution Preview

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

80-0.0002Q=40
0.0002Q=40
Q=40/.0002 =200000 units
P=80-0.0001*200000=$60

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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Calculate the order quantity in the given scenarios.

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).

a. Suppose the station plans to give away the videos. How many DVDs should it order? From which supplier?
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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