A firm uses two inputs to produce its output, capital (k) and labor (l)

The production function of the firm is given by y=f(k, l)=k^(1/3)l^(1/3)

The output market price is denoted by p and the input prices of capital and labor are denoted by r and w, respectively. There is perfect competition in the output market as well as in both input markets

a) Write down the input demand function for capital by solving the relevant optimization problem!

Fill in the blanks!

The input demand function for capital is k(p, r, w)=

A rm uses two inputs to produce its output, capital (k) and labor (I). l l The production function ofthe firm is given by'y = f (k, I) = k3 I3 . The output market price is denoted by p, and the input prices of capital and labor are denoted by r and w, respectively. There is perfect competition in the output market as well as in both input markets. b) Write down the input demand function for capital by solving the relevant optimization problem! Fill in the blanks! The input demand function for capital is k(p, r, w) = ApBrown where B = C= D =d) What is the firm's optimal short-run output level if r=14, w=24, and p=351