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Econ_181_HW2_S13_solution

D all landowners should support free trade e

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Unformatted text preview: d in fixed proportions as follows: To produce cloth requires 3 units of labor and 2 units of capital per unit output of cloth. To produce food requires 2 units of labor and 3 units of capital per unit output of food. Let L, K represent the total amount of labor and capital available in the economy. Let P! , P! denote the prices of output and let w, r denote the prices of labor and capital respectively. a) Find the production possibility frontier for the economy and sketch it. (Hint: it is defined by two linear inequalities that restrict total labor and total capital usage.) Answer: Labor constraint: 3Q ! + 2Q ! ≤ L since the technology implies L! = 3Q ! and L! = 2Q ! . Labor constraint: 3Q ! + 2Q ! ≤ L since the technology implies L! = 3Q ! and L! = 2Q ! . !"!!" !"!!" The intersection of the two constraints is given by ( ! , ! ), which is the production point. Q ! L 2 K 3 Feasible Production Set Q ! L 3 K 2 b) Show how an increase in the supply of capital shifts the PPF and the production point where both factors are fully used. (With Leontief technology and well- behaved utility function, there is a unique production point that represents full employment of both inputs.) Answer: An increase in capital shifts the capital constraint outward, as shown by the dashed line below. The economy are now producing more capital intensive good (F) and less labor intensive good (C). Q ! L 2 New Production Point K 3 Q ! L 3 K 2 c) Find input prices w, r in terms of output prices, assuming both goods are...
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