# A firm produces output according to a production function:Q = F(K,L) = min {4K,8L}.

November 24, 2016

I am provided with this information, what i still need is how to complete section b better. I dont understand why one unit of L is needed with 2 units of K.

2) (10 points) A firm produces output according to a production function:Q = F(K,L) = min {4K,8L}.a. (3 points) How much output is produced when K = 2 and L = 3?When K = 2 and L = 3, Q = 8 units. This is because this is a Leontief production function inwhich the inputs are used in fixed proportions. Using 2 units of capital will yield 8 units, andusing 3 units of labor will yield 24 units. The minimum of the two is 8 units, and so that is themost output that can be produced with this technology.

b. (4 points) If the wage rate is \$60 per hour and the rental rate on capital is \$20 per hour, what isthe cost-minimizing input mix for producing 8 units of output?The cost-minimizing mix of K and L that produce Q = 8 is K = 2, L = 1. This is because, theLeontief function dictates that only 8 units can be produced, so only 1 units of labor is necessary to produce this amount to go along with the 2 units of capital that set this minimum.

c. (3 points) How does your answer to part b change if the wage rate decreases to \$20 per hourbut the rental rate on capital remains at \$20 per hour?Since K and L are perfect complements in the production process, the cost-minimizing levels ofK and L do not depend on the rental rates of K and L. Therefore, the cost-minimizing levels of Kand L do not change with changes in the relative rental rates.

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