Cross Subsidies in Two Hypothetical Markets

Suppose a regulated firm produces two products, A and B. The market demands for the goods, expressed as the willingess of buyers to pay for them, are shown below. W2Pa and W2Pb are the willingness to pay for good A and B, respectively, and Qa and Qb are the quantities of the two goods.

W2Pa = 2000 - 10*Qa
W2Pb = 50 - (1/100)*Qb

On the supply side, the firm is willing to accept $1000 for each unit of good A. However, the government allows it to charge extra for good A in order to subsidize sales of good B. The extra charge on good A is $200 per unit, bringing the price paid by buyers to $1200. With the policy in place, the firm charges $10 for good B and sells 4000 units of it.

Please answer the following questions. You may assume that all of the extra revenue raised in market A is used to subsidize market B. You may also assume that the firm's supply curve for good B is perfectly elastic at $X, where X is initially unknown.

1. How large is the subsidy on each unit in market B? That is, how much higher would the price have to be without the subsidy?
2. Calculate the effect of the policy on consumer and producer surplus in both markets. Also calculate the amount of deadweight loss.

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