Question

4. Consider a firm that uses both labor and capital in production. The price of capital is $20 per unit and the wage rate is $10 per hour. Draw the firm's socost ine assuming a total production cost of $100. How steep is this line (that is, what is its slope)? Be sure to clearly label the axes. (3 points) b. Suppose the wage drops to S5 per unit. In which direction does the substitution effect change the firm's demand for labor and capital? In which direction does the scale effect change the firm's demand for labor and capital? (2 points) c. If the firm chooses its labor and capital combination to minimize its production costs, wl the marginal product of labor be higher than, lower than, or equal to the marginal product of capital? Why? (Assume that the price of labor and capital are those given in part b.) (2 points)

Answer 1

a) Taking number of units of labour on x axis and number of units of capital on y axis , given the budget of $100 and price of capital per unit = $20 maximum 5 units can be employed or 10 units of labour given the price of $10 per unit .

So iso-cost line = AB with slope = -price of labour / price of capital = - 10/20 = -1/2

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b ) if price of labour fall from $10 to $5 , the new iso-cost line will be AC such that firm can hire 20 units of labour if $100 spent on labour .

Substitution effect will cause the firm to substitute labour for capital as it is cheaper so demand for labour will increase and capital will fall. While the scale effect will cause the demand for both capital and labour to increase as firm can expand output and increase its profit as prices fall.

c ) since the prices of labour has fallen , firm will hire more labour to optimise its production cost and profits . Because of diminishing marginal product for a factor , marginal product of labour will be lower than the marginal product of capital given the prices in situation b .