PS2 solutions

PS2 solutions - Department of Economics University of...

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Department of Economics Fall 2010 University of California, Berkeley Economics 100B PS 2 Suggested Solutions Page  1 of 8 Suggested Solutions for Problem Set #2 1. (1 point total; ½ point each) Assume the production function is Cobb-Douglas. Assuming the production function is Cobb-Douglas means to assume that we have a multiplicative function, with  each factor of production raised to a power.  The sum of the powers must equal 1, which is what gives a Cobb- Douglas production function the property of constant returns to scale. For part a, use the formula  α - = 1 E L K L Y .   For part b, use the formula  ) ( E Y K L Y 1 - = a. What is the value of output per worker when K = 1,000,000; L = 500; E = 100; and   = 0.25? α a. Y/L =  75 0 25 0 100 500 000 000 1 . . ) ( , ,  = (2,000) 0.25 100 0.75  = 211.5 b. What is the value of output per worker when the capital intensity is 4, labor efficiency is 1,000, and   = 1/3? α b. Y/L =  ) , ( ) , ( / / 000 1 4 000 1 4 2 1 3 2 3 1 = = 2(1,000) = 2,000 2 .  (3.5 points total; ½ or 1 point each) a. (½ point) The definition of the balanced growth equilibrium is that what is balanced with what?  What is   the equation that expresses the balanced growth equilibrium condition? Definition:   Balanced growth equilibrium occurs when the growth rate of output per worker (Y/L) is balanced with  the growth rate of capital stock per worker (K/L). Equation:   The balanced growth equilibrium condition:   δ + + = g n s Y K   b. (½ point) Why are there two different equilibrium conditions given in the textbook: K/Y = s/  and K/Y = s/ δ (n+g+ )? δ The first BGE condition (K/Y = s/ ) is derived assuming that neither labor force nor labor efficiency is growing.  So δ   that condition applies only  in the special case where n = g = 0.  The second BGE condition (K/Y = s/(n + g +  ) ) δ   applies in general, and is the equation to use.
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Department of Economics Fall 2010 University of California, Berkeley Economics 100B PS 2 Suggested Solutions Page  2 of 8 c. (1 point) Suppose n = 0.01, g = 0.02,   = 0.04, s = 0.21,   =  δ α  and E = 1,000.  What is the value of the  capital-output ratio when the economy is in balanced growth equilibrium?  What is the balanced-growth- equilibrium value of output per worker? To find the value of the capital-output ratio when the economy is in balanced growth  equilibrium, we use the 
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This note was uploaded on 02/02/2012 for the course ECON 100B taught by Professor Wood during the Spring '08 term at Berkeley.

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PS2 solutions - Department of Economics University of...

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