Versarchery's production function is given by Q = L + K. The price of labor is...

 

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Versarchery's production function is given by Q = √L + K. The price of labor is w and the price of capital is r. First, consider Versarchery's production in the short run. Suppose the level of capital is fixed at K = Ko. For simplicity, suppose the fixed cost is sunk. (a) To produce Q units of output, what is the cost-minimizing choice of labor? How does the cost- minimizing choice of labor change with Q? With w? With r? (b) Derive the equation of the firm's short-run total cost function. How does the short-run total cost change with Q? With w? With r? Now, consider Versarchery's production in the long run. (c) Write down the cost-minimization problem. Derive the demand function for L and the demand function for K. Assume the firm will use both L and K in production. (d) Is labor a normal input? Is capital a normal input? Versarchery's production function is given by Q = √L + K. The price of labor is w and the price of capital is r. First, consider Versarchery's production in the short run. Suppose the level of capital is fixed at K = Ko. For simplicity, suppose the fixed cost is sunk. (a) To produce Q units of output, what is the cost-minimizing choice of labor? How does the cost- minimizing choice of labor change with Q? With w? With r? (b) Derive the equation of the firm's short-run total cost function. How does the short-run total cost change with Q? With w? With r? Now, consider Versarchery's production in the long run. (c) Write down the cost-minimization problem. Derive the demand function for L and the demand function for K. Assume the firm will use both L and K in production. (d) Is labor a normal input? Is capital a normal input?