After having started a highly unpopular war in Europe, the president of Leninslavia can only sell his country’s gas to two other friendly countries, which, in turn, are not sold gas by anybody else. These friendly countries are the poor nation of Kalininburg (KB) and the richer, morally-ambiguous Coconut Republic (CR). Given the geographical proximity between the two buyers, a strict ban on cross-border sales was agreed with the Kalinian government. The respective demand functions (in million units) for both countries are: QKB=10-PKB QCR=14-0.5PCR The total cost (TC), in millions too, depends on the total amount of units produced Q = QKB + QCR and also includes 10 million of fixed costs. TC follows the expression: TC=10+2Q+Q2 /8 i. Does Leninslavia meet the conditions necessary to implement price discrimination? Explain. ii. What should be Leninslavia’s profit-maximization strategy? Indicate prices and quantities, as well as the amount of social welfare generated. iii. Are the prices above consistent with the rule of elasticities? iv. Soon beginning to suspect of rampant corruption within the Kalinian government –some officials illegally withholding gas shipments to re-sell them to wealthy Coconutian industrialists, Leninslavia considers investing in additional security measures to prevent cross-country sales. How much at most should Leninslavia invest on that? v. Knowing that Leninslavia did not finally invest in extra security, now assume a second gas-exporting country, Argeline, is also willing to compete with her with so the relevant gas market (as per iv) becomes a duopoly. Gas being such a perfectly homogeneous product, the two sellers will split the demand and charge the same price, competing only on market share. If Argeline’s total cost function is TC=10+2Q+Q2 /20, determine the optimal quantities and market shares for both sellers. vi. Explain what would happen to the market as described in v) if it was suddenly discovered that 50% of the gas supplied by both sellers has excessive sulphur content
please could you help me with these questions. could you please separate each stage of the maths workings onto a different line so i can easily follow. many thanks
After having started a highly unpopular war in Europe, the president of Leninslavia can only sell his country’s gas to two other friendly countries, which, in turn, are not sold gas by anybody else. These friendly countries are the poor nation of Kalininburg (KB) and the richer, morally-ambiguous Coconut Republic (CR). Given the geographical proximity between the two buyers, a strict ban on cross-border sales was agreed with the Kalinian government. The respective demand functions (in million units) for both countries are:
QKB=10-PKB
QCR=14-0.5PCR
The total cost (TC), in millions too, depends on the total amount of units produced Q = QKB + QCR and also includes 10 million of fixed costs. TC follows the expression: TC=10+2Q+Q2 /8
i. Does Leninslavia meet the conditions necessary to implement
ii. What should be Leninslavia’s profit-maximization strategy? Indicate prices and quantities, as well as the amount of social welfare generated.
iii. Are the prices above consistent with the rule of elasticities?
iv. Soon beginning to suspect of rampant corruption within the Kalinian government –some officials illegally withholding gas shipments to re-sell them to wealthy Coconutian industrialists, Leninslavia considers investing in additional security measures to prevent cross-country sales. How much at most should Leninslavia invest on that?
v. Knowing that Leninslavia did not finally invest in extra security, now assume a second gas-exporting country, Argeline, is also willing to compete with her with so the relevant gas market (as per iv) becomes a duopoly. Gas being such a perfectly homogeneous product, the two sellers will split the demand and charge the same price, competing only on market share. If Argeline’s total cost function is TC=10+2Q+Q2 /20, determine the optimal quantities and market shares for both sellers.
vi. Explain what would happen to the market as described in v) if it was suddenly discovered that 50% of the gas supplied by both sellers has excessive sulphur content, which can corrode pipes and equipment. Buyers, which are risk-neutral, cannot tell the good gas from the bad gas and their demand for bad gas is Q=5-0.5P.
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