1.) A monopolist sells its good in two markets denoted by N and S. The demand...

1.) A monopolist sells its good in two markets denoted by N and S. The demand for the good in market N is PN = 100 − QN. The demand for the good in market S is PS = 60 − QS. The marginal cost of producing the good is $20. For your calculations below assume zero fixed costs. a (15). Derive the monopolist’s two-part pricing scheme that allows 1st-degree price discrimination. Provide the fixed fee, the per-unit price, and profit in each market. Calculate also the total welfare across the two markets. b (10). Derive the monopolist’s block-pricing scheme that generates the same profit as the two-part pricing scheme you obtained in (a).

Solutions

Expert Solution

The demand for the good in market N is PN = 100 − QN. The demand for the good in market S is PS = 60 − QS. The marginal cost of producing the good is $20.

Under the monopolist’s two-part pricing scheme that allows 1st-degree price discrimination, the fixed fee will be the amount of consumer surplus at the quantity P = MC and the price per unit is the marginal cost. Consumer surplus is given by CS = 0.4*(Max price – current price)*(current quantity)

Hence the fee to be charged in market N = 0.5*(100 – 20)*(100 – 20) = $3200 and the fee charged from consumers in market S = 0.5*(60 – 20)*(60 – 20) = $800. Price per unit is $20 in both markets. Profit from market N is $3200 and from N is $800. Total profit = $4000. Total welfare = CS + PS. Here there is no consumer surplus so welfare = $4000.

Under the monopolist’s block-pricing scheme that generates a profit of $4000, the monopolist will sell a package of several units at such a price that each market results in same profit as before. We see that CS in market N is $3200 and cost of production is 20*80 = $1600. Hence the block of 80 units will be available for $4800 (CS + cost of production). In the second market the same block will be made for 40 units at a price of package at $1600. From this scheme, revenue is $4800 + $1600 = $6400 and cost is (80 + 40)*20 = $2400 for selling a total of 120 units. Profit is therefore $6400 - $2400 = $4000.

Rahul Sunny answered 1 year ago

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