Question

Assuming that there are two types of radios on the market: good radios and bad radios. Of the firms that manufacture radios, 50% produce good radios and 50% produce bad radios. A good radio does not break for five years, while a bad radio has a 50% chance of breaking when it is first used. If the bad radio does not break immediately, it works for five years, just like the good radio. A good radio is worth $100 to consumers, and a bad radio is worth nothing.

a) What is the maximum price any consumer would be willing to pay for a radio if both types of firms produce radios? (1 mark)

b) If it costs $55 to manufacture each radio, will any firms want to produce radios?
 


c) If it costs $50 to manufacture each radio, which firms will want to produce radios?
 


d) Suppose that it costs $50 to manufacture each radio and $20 to repair a broken radio. Also suppose that the firms that produce good radios give a warranty in which they promise to repair any radio that breaks within five years of purchase. If the price of radios were to rise above $50, which type of firm would issue a warranty? If the price rose to $60, which type of firm would offer a warranty? Can warranties signal quality? What is the equilibrium price for radios in the market? 


Thank you for your generous help which would enlighten my knowledge on this subject and exercise.

Answer 1

a) $50

b) No firms will want to produce radios because they wouldn't want to sell at a loss ( 50 - 55 = - $5) whereas no buyer wants to pay more than $50.

c) Both firms will want to produce radios - both makes non-negative profit.

^ please correct Pt b above, it should be "If price less than $60 but greater than or equal to $50"

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Warranties alone cannot signal quality, since at prices greater than $60 both Bad Producers (strategically) and Good Producers (indifferently) offer warranty.

However combined with knowledge of relative price point, warranty can be a good indicator. If I have an estimate for the cost of manufacturing a radio and cost of repairing it, then I can say that if a seller is supplying the product for only a slight risk premium for warranty then it's likely a Good Seller and a high quality product.

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The Bad Producers are indifferent between selling without warranty at 50 and selling with warranty at 60, since in both cases they make zero profit overall.

The Good Producers prefer selling at $100 with warranty, because that's the absolute maximum a buyer will pay in a sure deal for a good radio.

Since buyers will pay more for a sure deal, the Bad Producers also charge $100 because on a bad unit they still come out with $30 profit. And there's no price competition preventing them from charging this high.

Thus an equilibrium price ratio is 1:1.

I wrote an because there are multiple equilibria, depending upon the nature of competition between the two firms.

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