Suppose you own a firm that producing shoes using both capital and labor. The production function is q=f(K, L)=0.5K2 L4 . In long run both capital (K) and labor (L) are variable. Price for each pair of shoes is $50 (p=50), the wage rate is 0.04 (w=0.04) and the rental price for capital is 1 (r=1). Given those output and input prices, what is the profit maximizing input level of K and L (K* & L* )?
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