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Rationing and Marginal Benefit to Consumers

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Please help with this problem. I'm not looking for a final answer, but I am definitely looking for the mathematical approach used. Thank you!

MB1=150-Q1 is the marginal willingness to pay, or marginal benefit, function for Consumer 1 who consumes Q1 of the commodity Q per month. For example, when Q1=1, MB=149, meaning that the consumer would be willing to pay at most 149 for 1 unit of consumption of good Q. MB for Q1 can be thought of as the marginal rate of substitution (MRS) for Q, in terms of the most the consumer would be willing to trade off in everything else (measured in $) for the consumption of Q. Under some strong assumptions, it can be thought of as the consumer's ordinary demand curve for good Q.

Similarly, MB2=75-.5Q2 is the corresponding marginal benefit function of good Q for Consumer 2.

a. Suppose these consumers live in Cuba and get a ration of 50 units of Q each month. What is the marginal willingness to pay at this level of consumption for each consumer? What is the total benefit each consumer receives from this policy-determined quantity ration?

b. Suppose these consumers enter the black market and illegally trade with one another. How much will they trade with each other, what will be their final level of consumption, and their MRS's in equilibrium? What will be the relationship between Q1 and Q2 be in ANY trading equilibrium involving these two consumers? What is the total benefit each consumer receives in the trading equilibrium? How does the total consumption benefit (sum of each consumer benefit) compare in this trading equilibrium with the total consumption benefit in the policy-determined quantity ration in the previous answer?

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Solution Summary

Marginal benefit used to determine impact of rations on an eceonomy

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You can calculate the the willingness to pay by inserting the rationed amount into the demand functions you are given. The marginal rate of substitution (MRS) is also the willingness to pay. Thus for consumer 1, you would have:
MRS= 150-50 = 100
and in the same way you would get 50 for consumer 2.

The total benefit is found by integrating the demand function from zero to the quantity obtained. Thus for the first consumer we ...

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