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Demand Curve / Marginal Products

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Question 1

Big Steel Co. is a price leader in the local steel market. The other, smaller manufacturers set their price based on that established by Big Steel. The following information has been gathered by Big Steel's pricing department.
Demand curve for steel is equation to
Qt = 10,000 - 0.5P
where Qt is the total amount of steel sold by all firms in the industry.
Big Steel's marginal cost curve is equal to MCb = 10,000 + 1.2 Qb
and the sum of the marginal cost curves for the other companies supplying the local market is
MCs = 0.5Qs
a. What is the effective demand curve facing Big Steel?
b. What is price should Big Steel set to maximize its profits?
c. How much steel will Big Steel sell? How much will its competitors sell?

Question 2

A firm uses two variable inputs, labor, L, and raw materials, M, with typically shaped isoquants. It pays $20 per hour for L and $5 per unit for M. At the current mix of L and M, the marginal products of L and M are:
MPl = 20
MPm = 4
Select the statement below that best describes the situation.

The firm is not minimizing costs because the ratio of the marginal product of labor to the price of labor is 1 and the ratio of marginal product of materials to the price of materials is 0.8. The firms should shift to using more L and less M to minimize costs.

The firm is not minimizing costs because the ratio of the marginal product of labor to the price of labor is 1 and the ratio of marginal product of materials to the price of materials is 1.25. The firms should shift to using more M and less L to minimize costs.

The firm is not minimizing costs. Because the price of labor is higher than the price of materials, the firm should use more M and less L.

There is not enough information to tell whether or not the firm is minimizing costs.

The firm is minimzing costs.

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Solution Summary

Demand Curve / Marginal Products

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1. Since Big Steel is a price setter, they will set the price first. All other small firms will follow that price and decide the amount of units they will produce. We assume that there are s small firms, and they collectively sell Qs. Then Qs + Qb = Qt.

The demand is Qn + Qb = 10000 - 0.5P or P = 20,000 - 2Qs - 2Qb.

For the followers, their collective revenue is Rev_f = (20,000 - 2Qs - 2Qb)Qs = 20,000Qs - 2Qs^2 - ...

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