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Economics: Demand and Supply at Kink

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The management of a firm believes that it faces a kinked demand curve. If it sets price above the kink in demand, its rivals will not match the price, and it will be operating on the demand curve:

P1 = 35 -0.005Q

If it sets price below the kink, management believes that it will be operating on the demand curve:

P2 = 50 - 0.015Q

If the firm's total cost curve is:

TC = 14,000 + 12Q + 0.002Q2

a) Determine the price, output, and profit that the firm earns when it sets price at the kink in demand.
b) What will be the output level for this firm if management sets price at \$30/unit, and rivals do not match the price increase? Assume that rivals are currently charging \$27.50 for similar products.
c) How much must marginal cost rise before this firm has an incentive to raise price above the price consistent with the kink in demand?
d) What will be the output level for this firm if management sets price at \$26 per unit, and rivals match the price decrease? Is this price feasible under current cost conditions?

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Solution Preview

The management of a firm believes that it faces a kinked demand curve. If it sets price above the kink in demand, its rivals will not match the price, and it will be operating on the demand curve:
P1 = 35 - 0.005Q
If it sets price below the kink, management believes that it will be operating on the demand curve:
P2 = 50 - 0.015Q
If the firm's total cost curve is:
TC = 14,000 + 12Q + 0.002Q2

a) Determine the price, output, and profit that the firm earns when it sets price at the kink in demand.

A kink, in demand, is a point, on the demand curve, where demand shifts. From the provided information two demand curves exist.

To determine the point of kink we set both demand curves equal and we get:
P1 = P2 = 35 - 0.005Q = 50 - 0.015Q
Price at kink = ...

Solution Summary

The problem set deals with topics under economics, specifically demand and supply at kink.

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