Please check my answers and correct them.
Pd = 20 000 – 20yd
MRd = 20 000 – 40yd
Pf = 25 000 – 50yf
MRf = 25 000 – 100yf
Firm’s production process shows Constant Returns to Scale and it takes $1,000,000 to produce 100 computers.
a. Find LAC (y) and MC (y). What do the graphs look like?
LAC (y) 1,000,000/100 = 10,000
MC (y) = 0
LAC is a horizontal line at 10,000 and since MC = 0, they share the same line.
b. If the firm maximizes its profits, how many computers for how much would it sell in both the domestic and foreign markets?
Sell 100 computers (since P = min LAC) for $18,000 (Pd = 20000 – 20(100)) in the domestic market and $20,000 (Pf = 25000 – 50(100)) in the foreign market.
c. What is the price elasticity of demand for both markets? Is demand more or less elastic in the market where the higher price is charged?
EDd = -20(18 000/100) = -3 600
EDf = -50(25 000/100) = -12 500
If higher price is charged, the demand is less elastic.
d. Suppose that somebody figures out a wiring trick that allows the firm’s computer build for either market to be costlessly converted to work in the other (ignore transportation costs). Given that the costs haven’t changed, how many computers should the firm sell and at what price should it charge? How will the firm’s profits change now that it can no longer practice price discrimination?
I don’t understand this question.
a) I disagree with your MC. Constant returns to scale (and no fixed costs) implies AC=MC. So, I think MC=10000
b) I disagree. Always Always Always, maximize by setting MC=MR. So, for the domestic 20000-40Yd = 10000. Solve for Yd. I get Yd=250.
(As a check, plug 250 into the demand equation and then calculate total profits. Compare that to your answer of Yd=100.)
Repeat for the Foreign market.
c) I disagree. In the domestic market, Yd=250, P=15000. Using the demand equation, bump up P by a small amount, say 1%. What is the %change Yd? I get Yd' = 242.5, a change of 7.5. and 7.5/250 = .03 or a 3%change. So the Price elasticity for domestic is 1%/-3% = -.3333.
Repeat for the foreign market.
d) I was also confused until I read the last sentence. Assume the firm can no-longer price discriminate -- that the price in the domestic market must equal the price in the foreign market. So, lets build the combined demand equation. Graphing, it will have a kink. Graphing the equation will be helpful to think about the problem
For prices above 20,000 it will sell only in the foreign market. At P=20000, Y=100. Draw a line starting at P=25000,Y=0 to P=20000, Y=100. Now then, at P=0 from the two demand equations, Yd=1000 and Yf=500, for a combined Y=1500. So draw a line from P=20000, Y=100 to P=0, Y=1500. The slope is 1400/-20000 = -14.2857. We have our demand curve. Extend this second piece back to the vertical axis. So, the relevant demand equation, I get, is P=21428 - 14.2857Y for Y>100.
So, MR will be 21428 - 28.5714Y
Set MC=MR and solve for Y.
posted by economyst