Please check my answers and correct them.
Domestic Market:
Pd = 20 000 – 20yd
MRd = 20 000 – 40yd
Foreign Market:
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.
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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.
a. To find the long-run average cost (LAC), you divide the total cost of production ($1,000,000) by the quantity of computers produced (100). So LAC = $1,000,000 / 100 = $10,000. The marginal cost (MC) is the additional cost incurred to produce one additional computer, and in this case, it is given as $0. Therefore, LAC is a horizontal line at $10,000 and MC is a straight horizontal line at $0 on the graph.
b. To maximize profits, the firm will produce and sell the quantity where price (P) is equal to the minimum of LAC. Since LAC is a constant $10,000 and MC is $0, the firm will sell 100 computers at a price of $10,000 each in both the domestic and foreign markets.
c. The price elasticity of demand (ED) is calculated by dividing the percentage change in quantity demanded by the percentage change in price. For the domestic market, the price elasticity of demand (EDd) is calculated as -20 * (18,000 / 100) = -3,600. For the foreign market, the price elasticity of demand (EDf) is calculated as -50 * (25,000 / 100) = -12,500. If the absolute value of the elasticity is greater than 1, demand is considered elastic. In this case, both markets have elastic demand since the absolute values of the elasticities are greater than 1. Demand is more elastic in the market with the higher price (foreign market) because the elasticity value is larger in absolute terms.
d. This question is asking what quantity and price the firm should sell its computers for now that it can freely convert them between the domestic and foreign markets without additional costs. Since the costs haven't changed, the firm will aim to maximize profits by selling at a price equal to the minimum of LAC, which is $10,000. Without price discrimination, the firm can sell as many computers as it can produce efficiently for $10,000 each. The profit for the firm will depend on the quantity that can be sold at that price and the production costs.