Consolidated Salt Company sells table salt to both retail grocery chains and commercial users (e.g.,bakeries,snack food makers,etc.).The demand function for each of these markets is:
$\begin{array} { l } \text {Retail grocery chains:}&P _ { 1 } = 180 - 8 Q _ { 1 } \\\text {Commercial users:}&P _ { 2 } = 100 - 4 Q _ { 2 }\end{array}$
where P₁ and P₂ are the prices charged and Q₁ and Q₂ are the quantities sold in the respective markets.Consolidated's total cost function (which includes a "normal" return to the owners)for salt is: $\mathrm { TC } = 50 + 20 \left( \mathrm { Q } _ { 1 } + \mathrm { Q } _ { 2 } \right)$ (a) Determine Consolidated's total profit function.
Assuming that Consolidated is effectively able to charge different prices in the two
(b) markets, what are the profit-maximizing price and output levels for the product in the two markets? What is Consolidated's total profit under this condition?
Assuming that Consolidated is required to charge the same price in each market, what are
(c) the profit-maximizing price and output levels? What is Consolidated's total profit under this condition?

Question

Consolidated Salt Company sells table salt to both retail grocery chains and commercial users (e.g.,bakeries,snack food makers,etc.).The demand function for each of these markets is:

\begin{array} { l } \text {Retail grocery chains:}&P _ { 1 } = 180 - 8 Q _ { 1 } \\\text {Commercial users:}&P _ { 2 } = 100 - 4 Q _ { 2 }\end{array}

where P₁ and P₂ are the prices charged and Q₁ and Q₂ are the quantities sold in the respective markets.Consolidated's total cost function (which includes a "normal" return to the owners)for salt is:

\mathrm { TC } = 50 + 20 \left( \mathrm { Q } _ { 1 } + \mathrm { Q } _ { 2 } \right)

(a) Determine Consolidated's total profit function.
Assuming that Consolidated is effectively able to charge different prices in the two
(b) markets, what are the profit-maximizing price and output levels for the product in the two markets? What is Consolidated's total profit under this condition?
Assuming that Consolidated is required to charge the same price in each market, what are
(c) the profit-maximizing price and output levels? What is Consolidated's total profit under this condition?

Quizplus · Accepted Answer

The Answer of Consolidated Salt Company sells table salt to both retail grocery chains and commercial users (e.g.,bakeries,snack food makers,etc.).The demand function for each of these markets is: $$\begin{array} { l } \text {Retail grocery chains:}&P _ { 1 } = 180 - 8 Q _ { 1 } \ \text {Commercial users:}&P _ { 2 } = 100 - 4 Q _ { 2 } \end{array}$$ where P₁ and P₂ are the prices charged and Q₁ and Q₂ are the quantities sold in the respective markets.Consolidated's total cost function (which includes a "normal" return to the owners)for salt is: $$\mathrm { TC } = 50 + 20 \left( \mathrm { Q } _ { 1 } + \mathrm { Q } _ { 2 } \right)$$ (a) Determine Consolidated's total profit function. Assuming that Consolidated is effectively able to charge different prices in the two (b) markets, what are the profit-maximizing price and output levels for the product in the two markets? What is Consolidated's total profit under this condition? Assuming that Consolidated is required to charge the same price in each market, what are (c) the profit-maximizing price and output levels? What is Consolidated's total profit under this condition?

Consolidated Salt Company Sells Table Salt to Both Retail Grocery