a. Suppose that we have D: p=10-q and S: p=q. Find the autarky equilibrium and the sum of consumer and producer surplus (CS and PS).
b. Suppose the world price is 4. Which party (consumers or producers) is no longer prepared to trade at the autarky equilibrium?
c. What form does the trade take? What is CS + PS now? Compare this with CS + PS before trade.
d. Does free trade with tariffs necessarily improve welfare? You can confine your attention to the case where the tariff still allow imports.
a. Show that a profit maximizing competitive firm chooses labour such that the real wage equals the marginal product of labour.
b. In a two sector labour market diagram, such as is typical for the Specific Factors model with mobile labour, labour moves until what is equalized?
c. By considering the equality in the last question, prove that in general equilibrium autarky producers and consumers are both behaving optimally in the Specific Factors model.
d. Suppose in a 2-good world (with goods X and Y) the production possibility frontier is Y=(1X2)1/2 and utility is given by the family of curves U=(X.Y)1/2 . Show by intuition, maths or graphs, what the autarky equilibrium is.
e. Find by intuition, maths or graphs what the marginal rate of transformation (mrt) and the marginal rate of substitution (mrs) at the autarky equilibrium are.
f. For the general case (not using the functions in (h)) show the effects of a tariff in general equilibrium. Prove that a tariff lowers welfare.
1. What is the point of having two sectors in the specific factors model rather than one? What policy question about trade is helped by this model rather than the Ricardian model.
2. Using a four quadrant derivation of the production possibility frontier (ppf), show what shape the ppf would have if both sectors have straight line production functions.
3. By considering the formula for the marginal rate of transformation (mrt), or otherwise, argue that your answer in (b) is reasonable.
4. In a two sector labour market diagram, illustrate how the diagram changes with the addition to one of the specific factors, with the initial labour allocation unchanged.
5. State what happens to wages in each sector if the labour allocation is not allowed to change.
6. Which direction would you expect labourers to move after the addition of a specific factor to one sector?
7. Show the equilibrium in a labour market diagram for a two sector Specific Factors model when the two sectors have constant and unequal values of marginal products of labour.
8. Using (c), or otherwise, show the situation described in (g) on a general equilibrium ppf.
9. Using (g) and (h) does Rybczinski’s theorem work for the case of a straight line ppf in general?
10. Discuss and illustrate the case where Rybczinski’s theorem works for a straight line ppf .
a. Does the assumption of labour mobility in response to wage differentials within an economy make sense to you as a literal description? Does it make sense as an approximation or generalization? What is the difference between an approximation and a generalization? (2 marks)
b. Assuming labour is homogenous with productivity determined by the fixedfactor/labour ratio, prove in a two-sector Specific Factors model labour market diagram that the addition of a fixed-factor in one sector raises output in that sector and lowers it in the other. What role does the movement of labour play in this proof? (2 marks)
c. Assuming the two-sector Specific Factors Model becomes a model of two countries, and that the price of output of both countries is unity (one). Initially assume a common wage across the world, due to free labour mobility (free immigration and emigration). Drawing on your answer to (b), what is the effect of capital accumulation in the developed world on world labour movements? (2 marks)
d. Do a welfare analysis of developed country capital accumulation in (c), and assume that worker welfare is the wage of each worker. (2 marks)
e. Assume now that from an initial equilibrium of equal wages we freeze labour allocations in the two countries. Do a welfare analysis of capital accumulation in the developed world. How does it compare with your analysis in (d), and what does it suggest would be the immigration-policy recommendation of a self-interested labour union in a developed country? (2 marks)