A cocoa shipping firm has determined that its US demand curve is given by: Q= 6,
ID: 1093310 • Letter: A
Question
A cocoa shipping firm has determined that its US demand curve is given by: Q= 6,500- 2P Where Q is metric tons of cocoa and P is the price per metric ton. The firm can import cocoa from the Ivory Coast for $1,150 per metric ton. Its shipping cost it $74 per metric ton of cocoa. The company has fixed costs of $1,100. A. Write the inverse demand function and illustrate with a simple diagram. B. Write the revenue function. At what level of output (Q) is revenue maximized. C. Display the profit function. D. Indicate the level of profits (or losses) if Q= 0 E. Determine the optimal price and quantity for this firm. F. Suppose the US government imposed an import tariff of $1,500 per metric ton cocoa. Compute the effect of the tariff on the optimal price and quantity sold by this firm. Does the tariff affect profits? Explain.
Explanation / Answer
a)
Q = 6500 -2P
2P = 6500 -Q
P = 3250 - Q/2
b)
Revenue = Q * P
= Q * (3250) - Q^2/2
= 3250 Q -Q^2/2
for the max output
DR/Dq = 0
3250 - Q = 0
Q = 3250 ........output at which revenue is maximized
c)
cost function = 1150 * Q + 74 * Q +1100 = 1224 Q + 1100
Profit = Revenue - cost
profit = 3250Q - Q^2/2 - 1224Q -1100
= 2026Q -Q^2/2 -1100
D)
If Q=0
loss = -1100
E)
for optimal price and quantity
DP/DQ = 0
2026 - Q = 0
optimal quantity = 2026
optimal price = 3250 - 2026/2 = 2237
F)
new profit function would be
profit = 2026Q -Q^2/2 -1100 - 1500Q = 526Q -Q^2/2 -1100
DP/DQ = 0
=> 526 - Q = 0
optimal quantity = 526
optimal price = 3250 - 526/2 = 2987
yes tariff decrease profit
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.