Economics Question

Suppose a firm has a production function of the following form: q=10*(4K+E)^(1/2) where q is the total output produced per week, K is the number of machines per week and E is the number of workers per week. This production technology implies that there are two inputs in the production function, labour and capital, and these two inputs are perfect substitutes. The (absolute value of the) slope of the isoquant (MPE / MPK) is 1/4. The firm wants to produce 200 units of output per week.

(a) Suppose the price of capital is $800 per machine per week and the weekly salary of each worker is $200. What

combination of inputs will the firm use?

(b)Suppose that there is a labour supply shock which results in a $25 reduction in the weekly wage rate. What combination of inputs will the firm use?

(c) What is the elasticity of labour demand as the wage falls from $200 to $175?

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