Nbspa production function with constant returns to scale

Question

Advanced International Trade Theory and Policy - NEED DONE TODAY 

1.  True or False with explanation (explanation determines credit). 
   1.  A production function with constant returns to scale can exhibit diminishing marginal product of its inputs.
   2. Suppose a production function only uses one input, labor.  If production displays constant returns to scale, then it does not exhibit diminishing marginal product of labor.
   3. Suppose a production function utilizes both capital (K) and labor (L) as inputs.  For this production function, an increase in L (holding K constant) leads to an exact proportional increase in output.  That is, for instance, increasing L by a factor of two yields twice as much output.  Then, this production function must display increasing returns to scale.

1.  Suppose, as with the "Workhorse" model in lecture, production in a 2-good (X,Y), 2-factor (L, K) economy exhibits constant returns to scale.  Unlike lecture, it so happens that X and Y have exactly the same factor intensity at all factor prices.  That is, there are no labor-intense or capital-intense goods here.
   1. What does the Efficiency Locus look like in the Edgeworth Box?  Sketch it and explain its particular shape.  (It will not look like the Efficiency Locus in the lecture.)
   2. What is the shape of the PPF that is implied by this particular Efficiency Locus?  Explain your answer.

1.  Using our "Workhorse" Model of Production and Trade as developed in lecture, suppose that a country is initially exporting good X. Its PPF then expands outward (we don't care about about precisely why), making it possible for it to produce more of both X and Y.  There are three possible ways the PPF could shift.  One where the PPF shifts out uniformly, and X and Y increase in the same proportion.  Second is a shift that is biased towards production of Y.  Finally, there is a shift that is biased towards X. Assume that the country is small enough that the world market price does not change as a result of its new PPF and production levels.
   1. Sketch a graph for each of the three possibilities listed above.  Include the PPF, the budget line, and indicate possible production/consumption points.  In particular, it will be helpful to follow the techniques from lecture about drawing these graphs, paying attention especially to how we identify the world price ratio and shift indifference curves.

Using your three graphs from part a, which (if any) of the following must be true, which might or might not be true, and which cannot be true?  Refer to your graphs to justify.

1. 1.  It will produce more of good X.
   2.  It will produce more of good Y.
   3.  Its income will rise.
   4.  It will import more of good Y.

1.  Use indifference curves as an indicator of national welfare to evaluate the following statement:  "Suppose the price of a country's exports increases relative to its imports.  This only benefits the country if it increases its quantity of exports in response.  If a country does not increase exports when their relative price rises, then the price incr ase will not increase welfare."  State your answer and explain in words.  You might use a graph to help in your explanatio