Question

A firm has two plants - one in Adelaide (A) and one in Brisbane (B). Let QA and QB denote the amounts of output produced in plants A and B respectively. Production functions in these two plants respectively are QA = 0.5LA QB = 0.1LE where LA and LB are the amounts of labour used in plants A and B respectively. Let wA and denote the price of labour in Adelaide and Brisbane respectively. Suppose wa = 1 and ws = I, where I = 2. (a) (1 point) Suppose production target is Q 20. To minimise costs, the firm would choose QA and QB = (b) (0.5 points) Suppose the firm's production target is revised downward to Q = 5. To minimise costs, the firm would choose QA = and QB

Answer 1

To minimize costs and meet a production target of Q = 20, the firm would choose the quantities of output QA and QB based on the given production functions. It involves solving an equation to find the optimal values of LA and LB and then substituting those values back into the production functions.

Step-by-step explanation:

The firm would choose the quantities of output QA and QB in order to minimize costs and meet a production target. To determine the optimal quantities, we need to set up a cost minimization problem and solve for the values of QA and QB. In this case, the production target is Q = 20, so we would set up the following equation: 0.5LA + 0.1LB = 20.For part (a), we can solve the equation to find the values of LA and LB. Once we have those values, we can substitute them back into the production functions QA = 0.5LA and QB = 0.1LB to find the quantities of output produced in each plant.