A firm uses two inputs, labour and capital, to produce an output x using a homothetic...

A firm uses two inputs, labour and capital, to produce an output x using a homothetic production technology. At the current market wage w, rental rate of capital r and output price p, the firm has identified A = (xA, ℓA, kA) as its profit-maximising production plan. In a diagram, with labour on the horizontal axis and capital on the vertical axis, use an isoquant and isocost diagram to illustrate this production plan and the set of all cost-minimising input bundles. Illustrate and explain the impact on the firm’s profit-maximising production plan of: (i) an increase in the wage rate; (ii) a fall in the output price. ()

(b)Explain how technological development affects a firm’s isoquant map and its long-run total cost of production. Illustrate your answer using appropriate diagrams. Assume the firm uses only two inputs, labour and capital, to produce its output, and uses a homothetic, decreasing returns to scale technology. )

Expert Solution

The firm's optimal choice of labor and capital is represented in the following diagram:

Where the red curve is the firm's isoquant for producing x units of output. The blue curve is the isocost curve representing the combinations of labor and capital which cost the same.

If the wage rate increases, the isocost curve will become steeper as the firm would be able to employ less labor for any given cost. This changes the firm's profit maximizing input choice:

The blue curve is the firm's new isocost curve and the purple curve is the firm's new isoquant for producing the new profit maximizing output. Note that this output is less than the firm's earlier choice because of the increase in price of labor.

For a fall in output price, the firm's profit will decrease for every input output combination. However, the firm was already maximizing profit for the given wage and rental rate irrespective of the price of the output. Therefore, the firm would continue to produce the same profit maximizing level of output.

Rahul Sunny answered 1 month ago

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