Citadelle, the Québec maple syrup producer, sells its syrup in Canada and in the

Question

Citadelle, the Québec maple syrup producer, sells its syrup in Canada and in the United States. The demand in Canada is given by P 36-QC, where P is the price ($ per litre) and QC is the quantity demanded (thousands of litres per year). The demand in the United States is given by P-40-as, where P is the price ($ per litre) and QUS is the quantity demanded (thousands of litres per year). The cost function is C 400,000 5Q, where C is the total cost (in $ per year) and Q is the total quantity produced (litres per year). Use these to answer questions 11-21 Suppose Citadelle cannot price discriminate. 11. Find the profit-maximizing quantity (in thousands of litres per year). 12. Find the profit-maximizing price (in $ per litre) 13. Calculate the consumer surplus (in thousands of $ per year) 14. Calculate the profits (in thousands of $ per year). Suppose Citadelle can practice the third-degree price discrimination 15. Find the profit-maximizing quantity in Canada (in thousands of litres per year 16. Find the profit-maximizing price in Canada (in $per litre). 17 Find the profit-maximizing quantity in the United States (in thousands of litres per year). 18. Find the profit-maximizing price in the United States (in $per ltre) 19. Calculate the combined consumer surplus (in thousands of $ per year). 20. Calculate the profits (in thousands of $ per year) 21. Is the third-degree price discrimination more efficient than uniform pricing?

Explanation / Answer

(11) In absence of price discrimination, Price in US = Price in Canada

In Canada, P = 36 - QCA

QCA = 36 - P

In US, P = 40 - QUS

QUS = 40 - P

Market demand (Q) = QCA + US = 36 - P + 40 - P = 76 - 2P

2P = 76 - Q

P = 38 - 0.5Q

C = 400,000 + 5Q

Marginal cost (MC) = dC/dQ = 5

Profit is maximized when Marginal revenue (MR) equals MC.

P = 38 - 0.5Q

Total revenue (TR) = 38Q - 0.5Q2

MR = dTR/dQ = 38 - Q

Equating with MC,

38 - Q = 5

Q = 33 (Thousand)

(12) When Q = 33,

P = 38 - (0.5 x 33) = 38 - 16.5 = $21.5

(13) From aggregate demand function, When Q = 0, P = $38 (Reservation price)

Consumer surplus = Area between demand curve & price = (1/2) x $(38 - 21.5) x 33 = 16.5 x $16.5 = $272.25

(14) Profit = TR - C

TR = P x Q = $21.5 x 33,000 = $709,500

TC = $(400,000 + 5 x 33,000) = $(400,000 + 165,000) = $565,000

Profit = $(709,500 - 565,000) = $144,500

NOTE: As per Chegg Answering policy, first 4 questions are answered.

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