The first column shows the number of donuts consumed, while the second and third

Question

The first column shows the number of donuts consumed, while the second and third columns (respectively) show Shane’s and Miriam’s marginal personal use values. Assume that Shane’s initial endowment is three donuts, while Miriam’s initial endowment is 13 donuts. Suppose that Miriam is allowed to set the price at which Shane can purchase additional donuts (beyond his initial endowment of three donuts). What price would Miriam set if her objective were:

To maximize her Total Revenues (that is, the number of donuts Shane purchases multiplied by the price set by Miriam);

To maximize Miriam’s Producer Surplus (that is, Total Revenues minus Miriam’s Total Costs, defined as her cumulative opportunity cost of selling donuts to Shane rather than consuming them herself);

To maximize Shane’s and Miriam’s Total Surplus (that is, Consumer Surplus plus Producer Surplus)

For each case, provide both your answers and a brief explanation of how you derived it

Number of Donuts Shane's       Marginal Personal Use Value Miriam's       Marginal Personal Use Value 0 $0.00 $0.00 1 $2.00 $1.50 2 $1.90 $1.45 3 $1.80 $1.40 4 $1.70 $1.35 5 $1.60 $1.30 6 $1.50 $1.25 7 $1.40 $1.20 8 $1.30 $1.15 9 $1.20 $1.10 10 $1.10 $1.05 11 $1.00 $1.00 12 $0.90 $0.95 13 $0.80 $0.90 14 $0.70 $0.85 15 $0.60 $0.80 16 $0.50 $0.75 17 $0.40 $0.70 18 $0.30 $0.65 19 $0.20 $0.60 20 $0.10 $0.55 Initial allocations

Explanation / Answer

Here in this case, Miriam is producer and Shane is consumer.

Shane's marginal personal use value can be considered as Shane's marginal cost or it is marginal revenue for Miriam. And Miriam's marginal personal use vallue can be considered as her marginal cost.

(a) If objective is to maximize Total revenue.

Here only TR should be maximum irrespective of the cost that Miriam may incurred by selling them. We find out that by selling 10 donuts, which could be sell at $1.1 per donuts, Miriam will get maximum revenue from other combinations. Thus Miriam will set price at $1.1 and 10 donuts will be sold giving maximum revenue of $11 to Miriam.

(b) If objective is to maximize Total Profit = TR - Total cost

At maximum Profit, MR = MC.

At 11 donuts price is set at $1.

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