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A tannery has a cost l2l2 of tanning ll tons of leather
A tannery has a cost l2l2 of tanning ll tons of leather. Tanned leather can be sold at $100 per ton. The tannery maximizes profits. The tanning process gives off unpleasant smells. Each ton of leather processed by the tannery has a social cost of $10( How much the neighborhood is willing to pay to avoid the smell).
a. Assuming the tannery ignores the effect of the smell, how much will it produce?
Expert Solution
a)
The cost functions for a tannery:
C=l2C=l2
Where:
l is the quantity of leather.
Calculation of Marginal cost:
MC=C′=2lMC=C′=2l
The price of tannery is 100 dollars per unit.
The total revenue and marginal revenue function for the tannery:
TR=P×lTR=100lMR=TR′=100TR=P×lTR=100lMR=TR′=100
Since the firm is ignoring the effect of the smell, it will consider only its marginal revenue and marginal cost for the production purpose. So, it will produce the output level where marginal revenue becomes equal to marginal cost.
Using the above condition:
MR=MC100=2ll=50MR=MC100=2ll=50
So, the firm will produce 50 units of tannery to maximize its profits.
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