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Unformatted text preview: Exam ARE 201 (International Trade) 2007. Answer all parts of all three questions (see reverse) Answer Key 1) Consider the problem y ( α ) = max x g ( αx ) α where α is a parameter. Denote x ∗ ( α ) as the solution to this problem. (a) (10 points) Write the expression for the elasticity of x ∗ with respect to α. (b) (10 points) Write the expression for dy dα . Answer 1 a) Denote x ∗ ( α ) as the solution to this problem. The f rst order condition is αg ( αx ) α = g ( αx ) = 0 . Taking the di f erential and setting it equal to 0 gives g 00 ( αx ) xdα + g 00 ( αx ) αdx = 0 . This equation implies dx ∗ dα = − x ∗ α . Convert to elasticity to obtain dx ∗ dα α x ∗ = − 1 b) Using the envelope theorem and the quotient rule we have dy dα = αg ( αx ) x − g ( αx ) α 2 = − g ( αx ) α 2 = − y α 1 Some people gave as the answer for part "a" dx dα x α . I wasn’t asking whether you knew the formula for the elasticity; I wanted to see whether you could apply it. If I had asked for an expression for the derivative of x ∗ with repect to α , would you have written dx ∗ dα ? 1 2) In a two commodity world (food and cloth) Home imposes an ad val- orem production tax τ on cloth, returning tax revenues to consumers in a lump sum. Home moves from autarchy to free trade, keeping the tax con- stant. Food is the numeraire good, and p is the consumers’ relative price of cloth. 2 a) (5 points) Denote the equilibrium levels of production of food and cloth in autarchy as F and C . Denote as y the level of national income. What is the value of y ? (Write the equation for y in terms of the notation given above.) b) (15 points) State and brie f y explain a su ﬃ cient condition under which the movement to free trade increases Home’s welfare....
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This note was uploaded on 08/01/2008 for the course ARE 201 taught by Professor Karp during the Fall '07 term at University of California, Berkeley.
- Fall '07