Each ton of ore mined from the Baby Doe Mine in Leadville, Colorado, produces one ounce of silver and one pound of lead in a fixed 1:1 ratio. Marginal costs are $10 per ton of ore mined.
The demand and marginal revenue curves for silver are
PS = $11 - $0.00003QS
MRS = ∂TRS/∂QS = $11 - $0.00006QS
And the demand and marginal revenue curve for lead are
PL = $0.4 - $0.000005QL
MRL = ∂TRL/∂QL = $0.4 - $0.00001QL
Where QS is ounces of silver and QL is pounds of lead.
A. Calculate profit-maximizing sales quantities and prices for silver and lead.
B. Now assume that wild speculation in the silver market has created a fivefold (or 500%) increase in silver demand. Calculate optimal sales quantities and prices for both silver and lead under these conditions.