X is a u.s. manufacturer of digital controls for milling machines. the firm has
ID: 1223185 • Letter: X
Question
X is a u.s. manufacturer of digital controls for milling machines. the firm has been exporting its least expensive model, which sells for us$1,500 to Mexico, where the demand has proved to be Q= 3,500 - 2P, where Q= quantity demanded and P= price. X wants to break into the south american markets in Brazil, Argentina and chile. if the demand in each of these countries is the same as in Mexico,
a. how many machines can X sell in all three countries?
b. at a price of $1,500, what will be the total revenue, TR, from sales in all three countries?
c. what is the price elasticity of demand in each country when the price is $1,500?
d. if the price is $1,500, what will be the marginal revenue, MR, in each country?
e. how many units must X sell in each country in order to maximize revenue? what would be the price?
f. what will the price elasticity be when total revenue is maximized
answer with explanation
Explanation / Answer
a) The total (market) demand function for all the three countries is: Q= 3(3,500 - 2P)
Q = 10,500 - 6P
If P = $1500
Q = 10,500 - 6(1500) = 1500 units
Thus, X can sell 1500 units in all three countries.
b) TR = P * Q = $1500 * 1500 = $2,250,000
c) when the price is $1,500 , each country's quantity is:
Q = 3,500 - 2P = 3,500 - 2(1500) = 500 units
PED = Q/P * P / Q (where Q/P = price coefficient = -2)
= -2 * 1500 / 500 = -6
d) The inverse demand function is:
P = 1750 - 0.5Q
TR = P * Q = 1750Q - 0.5Q2
MR = 1750 - Q
e) TR will be maximized when MR = 0
=> 1750 - Q = 0
=> Q = 1750
and, P = 1750 - 0.5Q = 1750 - 0.5(1750) = $875
f) PED = Q/P * P / Q (where Q/P = price coefficient = -2)
= -2 * 875 / 1750 = -1
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