Suppose you are the production manager of a firm that has a production function: Q = (K )(L^0.5) where Q represents the firm’s level of output, K is the number of units of capital you utilize, and L is the number of units of labour you hire. The rental rate of a unit of capital is given by r = $100, and the wage rate for a unit of labour is given by w = $10. The firm operates in a competitive market where its output can be sold for $100 per unit. (a) Suppose the firm is operating in the short run, with its capital fixed at K = 1. What level of Q will maximize its profits? (b) Now suppose that in the long run, the firm can set its capital to be either K=1 or K=2. What would you recommend in order to maximize profit?
Suppose you are the production manager of a firm that has a production function:
Q = (K )(L^0.5)
where Q represents the firm’s level of output, K is the number of units of capital you utilize, and L is the number of units of labour you hire. The rental rate of a unit of capital is given by r = $100, and the wage rate for a unit of labour is given by w = $10. The firm operates in a competitive market where its output can be sold for $100 per unit.
(a) Suppose the firm is operating in the short run, with its capital fixed at K = 1. What level of Q will maximize its profits? (b) Now suppose that in the long run, the firm can set its capital to be either K=1 or K=2. What would you recommend in order to maximize profit?
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