03 Jun Question Q1. A firms production process uses
Question
Q1. A firms production process uses labour, L, and capital, K, to produce an output, Q according to the function Q = 25KL. Let labour be fixed at level L L . What is the cost minimizing level of capital that the firm must use to produce a target level of output, Q Q ? [6 marks]
Q2. Given a high elasticity of substitution between capital and labour, what does this imply about
the elasticity of demand for labour? [2 marks]
Q3. Suppose that a firms production function of output Q is a function of only two inputs, labour
(L) and capital (K) and can be written Q = 5LK. Letting the wage rate for labour be w and the
rental rate of capital be r,
a. Dervie the equation for the firms demand for labour. [6 marks]
b. Let the wage rate for labour be w = 10 and the rental rate of capital be r= 10. If the firm
produces 1000 units of output, how many units of labour will it use? [4 marks]
Q4. A firms production function is given by Q K 2 L . The wage rate is w $10 and the rental
rate of capital is r $20 .
a. What is the most efficient combination of labour and capital ( L, K ) if the firms budget is
$1,200? [4 marks]
b. How much output can the firm produce? [4 marks]
Q5. The production function for a good is given by:
Q = 2 min{L, K}
a. Draw an isoquant for Q =20 and Q = 40 [4 marks]
b. If the wage rate, w, is $20 per hour and the rental cost of capital, r, is $40 per hour and the firms total cost of producing 40 units? [2 marks]
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