$1.$Kiteland $($K$)$ and Airland $($A$)$ are two economies with total labour of $50$ and $150,$ respectively. The tastes and preferences of these economies, over the two goods X and Y$,$ are the same and are given by the utility function U$($X$,$ Y$)=$ X $^0\mathrm{.}6*$ Y $^0\mathrm{.}4$ In Kiteland, one unit of labour can produce $3$ units of Good X; while it can produce $5$ units in Airland. Similarly, one unit of labour can produce $4$ units of Good Y in Kiteland, whereas it can produce $8$ units in Airland. Given this information, answer the following questions:

What is the opportunity cost of producing X in terms of Y in Kiteland and Airland?

$($ii$)$ What are the production possibility frontiers for the two countries?

$($iii$)$ Under the conditions of free trade, what is the equilibrium relative price?

$($iv$)$ Discuss whether the economies would go for complete specialization?

$($v$)$ If there was complete specialization, what would have been the relative output of X to Y produced?

$2.($a$)$ In the world economy, there are two countries: Gangaland and Missisippiland. Gangaland has a preference for consumption in the future and Missisippiland has a preference for consumption in the present. Illustrate how trade is intertemporally balanced with the help of diagram$($s$).$

$($b$)$ Consider two countries A and B$.$ The real wage rate in Country A is higher than the real wage rate in Country B$.$ How would international trade affect real wages between them if labour is perfectly mobile across the two country

$3.($a$)$ Consider a standard Heckscher$-$Ohlin $($HO$)$ Model, where two countries Home and Foreign produce two goods, sugar and milk, using labour $($L$)$ and capital $($K$).$ Home is relatively labour abundant and Foreign is relatively capital abundant. Assume that sugar is relatively capital intensive and milk is relatively labour intensive. Answer the following questions:

$($i$)$ Discuss the pattern of trade between the two countries.

$($ii$)$ Under what condition$($s$)$ factor price equalization may be obtained? Discuss with the help of a diagram, showing the segment of equalization.

$($b$)$ Discuss the domestic market failure argument against free trade with the help of a diagram.

B$.$ Write a short note on optimum tarriff

$4.($a$)$ Countries A$,$ B and C are the only three computer$-$ producing countries in the world. The three countries have the same production technology for every firm, and face the same demand conditions. The annual sales of the three countries are $10,00,000$; $90,00,000,$ and $40,0,00$ dot $0$ computers, respectively. Fixed and marginal costs of production of computers for each firm in each country are $750,000$ and $5000,$ respectively; and the degree of responsiveness of each firm's sales to its price, vis$--$vis other firms is $1/330,000.$ Answer the following questions:

$($i$)$ Calculate the equilibrium number of firms in the three countries before trade.

$($ii$)$ What is the equilibrium price in these countries under autarky?

$($iii$)$ Calculate the total number of firms and the equilibrium price, after the economies integrate.

$($iv$)$ Discuss the gains from trade of market integration post trade. Which country gains the most from integration?

B$.$ Write a short note on leontief paradox

$5.$ Consider a firm in an imaginary country Compland producing computers, using computer engineers $($E$)$ and production workers $($P$).$ Computer engineers are engaged in designing computer software, while production workers are engaged in the assembling of computer components. Computer engineers are considered to be highly skilled personnel and earn relatively higher salaries $($W$\_\{$E$\})$ compared to production workers $($W$\_\{$p$\})$

$($i$)$ Starting from no$-$trade equilibrium with a production possibility frontier $($PPF$)$ of a firm, illustrate the gains from offshoring, if Compland has a comparative advantage in providing the services of the production workers.

$($ii$)$ Now suppose that advances in engineering design in the rest of the world decrease the relative salaries of computer engineers. Illustrate and discuss the implications of this change in the production of computers in Compland, with the help of a diagram.

$6.($a$)$ Autoland wants to set up an automobile industry.

The free trade price of an automobile is $$8000$ and the imports of auto$-$components which go into the making of an automobile are priced at $$4000.$ Answer the following questions:

$($i$)$ If the government imposes an ad valorem tariff of $20$ percent on automobile imports, what is the effective rate of protection $($ERP$)$ offered to the industry?

$($ii$)$ Suppose Autoland wants to set up its own auto$-$components industry and hence the government imposes an ad valorem tariff of $10$ percent on imports of auto$-$ components, with no tariffs on automobiles. What would be the new ERP offered to the automobile industry?

$($iii$)$ In continuation to Part $($i$),$ now suppose, the government of Autoland imposes an ad valorem tariff of $10$ percent on imports of auto$-$components along with the existing tariff on automobiles. What would be the new ERP offered to the automobile industry?

$($iv$)$ Critically analyze which of the three policies used by the government of Autoland to develop its own automobile industry, protects the domestic automobile producers the most.

B$.$ Consider two countries: Fineland and Sineland, producing two goods: mobiles and iPods, under perfectly competitive market conditions. Fineland exports mobiles and imports iPods. Sineland exports iPods and imports mobiles. Assuming well$-$ behaved offer curves for both the countries, illustrate with help of a neatly labeled diagram, as to what would happen if there is sudden fall in the supply of iPods by Sineland?

$7.$A$.$Consider a large open economy Paperland exporting paper. Discuss the net welfare implications of an export tariff on paper imposed by Paperland with the help of a diagram. Is there any rationale for the domestic producers of Paperland to oppose this export tariff imposed?

B$.$ Consider Country A producing Good X which imposes a negative externality in the form of pollution. With the opening up of the economy for free trade, Country A becomes an importer of Good X$.$ Illustrate with the help of a diagram how free trade of Good X might make this country better off.

$8($a$)$ For the given costs and benefit curves of lobbying, the endogenously determined tariff rate of protection is t $*$Suppose the cost of lobbying decreases. What will happen to the optimal protection rate? Illustrate with the help of a diagram.

$($b$)$ Consider two countries A and B$.$ producing homogenous goods and competing in a Cournot Duopoly setup in intra$-$industry trade. Suppose Country B grants an export subsidy of$.$ Illustrate with the help of a diagram the change in the reaction functions of the two countries and comment on the pattern of trade.