Production problem: Optimal Input Combinations

Government output is sometimes considered fixed, with a goal of minimizing the cost of providing that output. Thus, it is thought that when faced with an increase in the cost of labor, government costs go up in the short run, but adjust downward in the long run. Suppose the output for government production is given by the function G = 2lnL + 4lnK, where G is the amount of government produced, L is the amount of labor used, K is the amount of capital used and ln indicates the natural logarithm. We assume that the price per unit of labor is 2 and the price per unit of capital is 4. [HINT: The MPK=1/K and MPL=1/L]

a) Find the efficient combination of K and L. 

b) If G=24, find the amounts of K and L that should be used.