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A cocoa shipping firm has determined the its U.S demand curve is given by: Q=7,500-3P where...

A cocoa shipping firm has determined the its U.S demand curve is given by: Q=7,500-3P

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 $1,850 per metric ton. It's shipping cost is $104 per metric ton of cocoa. The company has fixed costs of $2,000.

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 profit (or losses) if Q=0

e. Determine the optimal price and quantity for this firm.

f. Suppose the U.S government imposed an import tariff of $270 per metric ton of cocoa. Compute the effect of the tariff on the optimal price and quantity sold by this firm. Does the tariff affect profits? Explain.

Solutions

Expert Solution

The demand curve is given by: Q=7,500-3P, Q is metric tons of cocoa. The firm has import cost of $1,850Q and the shipping cost is $104Q. Hence total variable cost is 1954Q. The company has fixed costs of $2,000. The cost function is C(Q) = 2000 + 1954Q. Marginal cost is 1954.

a. The inverse demand function and is

Q = 7500 - 3P

3P = 7500 - Q

P = 7500/3 - Q/3

P = 2500 - Q/3

This is the inverse demand function.

b. The revenue function is R = PQ = 2500Q - Q^2/3

Find the level of output (Q) when revenue is maximized by keeping the MR function = 0

MR = 0

2500 = 2Q/3

Q(revenue maximizing) = 3750 units.

c. The profit function is Π = revenue - cost

Π =  2500Q - Q^2/3 - 2000 - 1954Q

= 546Q - Q^2/3 - 2000

d. if Q=0, then there is a loss of fixed cost amounting to 2000.

e. Find the optimal price and quantity for this firm by placing marginal profit = 0

MP = 0

546 = 2Q/3

This gives Q(profit maximizing) = 819 and price(profit maximizing) = 2500 - 819/3 = $2227

f. Suppose the U.S government imposed an import tariff of $270 per metric ton of cocoa. The new cost function will be C(Q) = 2000 + (1954 + 270)Q and so MC rises by 270. The new profit function is 276Q - Q^2/3 - 2000. Find the new quantity and price using marginal profit = 0

276 = 2Q/3

Q(new) = 414 and price = $2632

New profit is 276*414 - (414^2)/3 - 2000 = 55132. Yes profits are reduced from $221857 to $55132

Rahul Sunny answered 2 years ago
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