Citadelle, the Québec maple syrup producer, sells its syrup in Canada and in the
ID: 1148171 • Letter: C
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.