Question

when inputs K, L, are perfect complements, the isoquant is L-shaped, draw the graph, and then show in the graph that increases in the wage rate cause only scale effect but no substitution effect. Also, will there be any differences between the short-run labor demand curve and the long-run labor demand curve?

Answer 1

Isoquant line gives all capital-labour combinations that produce the same level of output while the isocost line is the locus of all the possible combinations of labour and capital that a firm can utilize for same budget. the tangency of isoquant line and isocost line gives the equilibrium.

The slope of isoquant line = MP_L/MP_k and slope of isocost line = w/r

Where, MP_L is the Mrginal Product of Labour, MP_k is the Marginal product of capital, w = wage rate and r=rental cost of capital

If K and L are perfect complements, the isoquant line is L shaped, which means that the production is done with a fixed proportion of K and L. If the firm has more K than the required proportion, Firm will be indifferent because the output can be produced only in fixed proportion of k and L. Therefore, the equilibrium is at the kink (right angle) where the isocost line is tangent to the isoquant line as shown in the graph below:

If w increases, isocost line becomes steeper due to higher slope and the labour becomes relatively expensive than capital. Firm will higher less labour (scale effect). However, firms will have to reduce K as well in order to produce output because k and L are perfect complements and are needed in fixed proportion to produce output. Therefore, both K and L decline and firm moves to a lower isoquant line (only scale effect) where the ratio of K/L is fixed. The movement is shown in the above graph. The original equilibrium is at E1, as wage increases to w', isocost line becomes steeper due to higher slope and the new equilibrium is at E1. Both K and L decrease in same proportion (scale effect) and there is no substitution effect due to fixed proportion production function.

The short-run demand curve for labour indicates change in firm's employment due to change in wage rate keeping K constant and is given by Value of Marginal Product (VMP_L) = MP_L*P, where P= Price of the good. the curve is downward sloping because marginal product eventually declines due to law of diminishing marginal utility. A rise in the wage, decreases the firm’s employment due to higher cost.

The long-run demand curve for labour gives the firm’s employment at a given wage and is downward sloping. If the wage rate increases, two effects work: scale effect i.e. firm reduces employment due to higher cost, firm change mix of inputs by substituting for capital for Labour (substitution effect). Since, here k and L are perfect complements and therefore, substitution effect is zero, rise in wages reduces employment.