Suppose that your firm is the only producer of a high-tech sports utility vehicl
ID: 1168802 • Letter: S
Question
Suppose that your firm is the only producer of a high-tech sports utility vehicle for North American markets. Assume a constant marginal cost of $25,000 to produce each vehicle and no fixed costs of production.
a) The US demand for the vehicle is given as QUS = 18,000 - 400 PUS where price is in thousands of dollars. Supposing your firm supplies the US only, what quantity of vehicles should you produce, what price will you charge, and what profits will you make?
b) The Canadian demand for the vehicle is given as QCAN = 8,000 - 100 PCAN where price is in thousands of (US) dollars. Supposing your firm supplies Canada only, what quantity of vehicles should you produce, what price will you charge, and what profits will you make?
c) Suppose now that your firm is a US company, but that you can freely export vehicles to the Canadian market. Suppose also that you can make a Canadian version of the vehicle and a US version, so that the markets are completely separate (i.e., the conversion of a Canadian vehicle to a US version is very expensive, and vice versa). What quantity of vehicles should you produce and sell in Canada, what quantity of vehicles should you produce and sell in the US, and what will your profits be?
Explanation / Answer
Solution :
a) US demand for the vehicle is given as QUS = 18,000 - 400 P US
400 P = 18,000 - Q
P = 45 - 0.0025 Q
Revenue = (45 - 0.0025Q) Q
Revenue = 45 Q - 0.0025 Q2
Marginal revenue = 45 - 0.005 Q
The profit maximizing price and quantity produced by the firm is calculated by equating marginal revenue and marginal cost
Marginal revenue = marginal cost
45 - 0.005 Q = $ 25,000
-24955= 0.005Q
Q = 4,991,000 units to be produced
Price = 45 - 0.0025 Q
P = 45 - 0.0025 X 4,991,000
Price = $ 12,433 to be charged for each high-tech sports utility vehicle in the US market .
Profit = $ 12,433 X 4,991,000 - $ 25,000
Profit = 6.20 X 10 10
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b) The Canadian demand for the vehicle is given as QCAN = 8,000 - 100 PCAN
PCAN = 80 - 0.01 QCAN
Revenue = Price X quantity
Revenue = ( 80 - 0.01 Q ) Q
R = 80 Q - 0.01 Q 2
Marginal revenue = 80 - 0.02 Q
Equating marginal revenue = marginal cost
80 - 0.02 Q = $ 25,000
Q = 1,246,000 units to be produced in Canadian market
Price = 80 - 0.01 Q
Price = 80 - 0.01 X 1,246,000
Price = $ 12,380 to be charged for each sports utility vehicle in Canadian market .
Profits = Revenue - cost
Profits = Price X quantity - cost
Profits = $ 12,380 X 1,246,000 - $ 25,000
Profits = 1.542X 10 10
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c) The total market demand is given by Qd = 18,000 - 400 PUS + 8,000 - 100 PCAN
Qd = 26,000 - 500 P
P = 52 - 0.002 Q
Revenue = Price X quanity demanded
Revenue =( 52 - 0.002 Q ) Q
Revenue = 52 Q - 0.002 Q2
Marginal revenue = 52 - 0.004 Q
Equating marginal revenue & marginal cost
52 - 0.004 Q = 25,000
Q = 6,237,000 units to be produced .
Price = 52 - 0.002 Q
Price = $ 12,422 to be charged
Out of 6,237,000 units that is produced , 1,246,000 units to be produced and sold in Canadian market and 4,991,000 units to be produced and sold in US market .
Profits = Revenue - cost
Profits = 6,237,000 X $ 12,422 - $ 25,000
Profits = 7.74 X 10 10
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