Assume that the demand function for tuna in a small coastal town is given by 100 p = q0.5 (200 s q s 800), where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in one month. (a) Calculate the price (in $ per Ib) that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month. per Ib (b) Calculate the monthly revenue R (in dollars) as a function of the number of pounds of tuna q. R(g) = (c) Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of 400 pounds per month. revenue $. marginal revenue $ per Ib of tuna Interpret the results. At a demand level of 400 pounds per month, the revenue is $ per additional pound of tuna. and increasing at a rate of $

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Author:James Stewart, Lothar Redlin, Saleem Watson
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MY NOTES
Assume that the demand function for tuna in a small coastal town is given by
100
p =
g0.5
(200 s q s 800),
where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in
one month.
(a) Calculate the price (in $ per Ib) that the town's fishery should charge for tuna in order to produce a demand of
400 pounds of tuna per month.
24
per Ib
(b) Calculate the monthly revenue R (in dollars) as a function of the number of pounds of tuna q.
R(q) =
(c) Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of
400 pounds per month.
revenue
marginal revenue
$4
per Ib of tuna
Interpret the results.
At a demand level of 400 pounds per month, the revenue is $
per additional pound of tuna.
and increasing at a rate of $
(d) If the town fishery's monthly tuna catch amounted to 400 pounds of tuna, and the price is at the level in part (a),
would you recommend that the fishery raise or lower the price of tuna to increase its revenue?
O raise the price
O lower the price
Transcribed Image Text:MY NOTES Assume that the demand function for tuna in a small coastal town is given by 100 p = g0.5 (200 s q s 800), where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in one month. (a) Calculate the price (in $ per Ib) that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month. 24 per Ib (b) Calculate the monthly revenue R (in dollars) as a function of the number of pounds of tuna q. R(q) = (c) Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of 400 pounds per month. revenue marginal revenue $4 per Ib of tuna Interpret the results. At a demand level of 400 pounds per month, the revenue is $ per additional pound of tuna. and increasing at a rate of $ (d) If the town fishery's monthly tuna catch amounted to 400 pounds of tuna, and the price is at the level in part (a), would you recommend that the fishery raise or lower the price of tuna to increase its revenue? O raise the price O lower the price
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