Income Distribution between Fixed factor and Variable Factor

With th MRP and ARP, we can find the income distribution between a fixed factor, e.g. land, and a variable factor, e.g. labour.

From fig 1, WE is the equilibrium wage rate. The total revenue product is ARP1 * QE, while the total wage payment is WE * QE (income to labour). The difference between TRP and total wage payment is the imputed rent to the use of the fixed factor (income to land).

What will happen if there is a decrease in labour supply? (the adjustment of the income distribution between land and labour)

A decrease in labour supply will increase the wage rate of labour. The total wage payment (total labours' income) may increase or decrease, depending on the demand elasticity of labour, but the imputed rent earned by land (income to land) must decrease. Moreover, the decrease in labour supply will also increase the average revenue product of labour. (The answer of increasing in labour supply is vice versa.)

If the use of labour is reduced by law, how does it affect the marginal productivity of land and labour?

Because of diminishing returns, if the use of labour is reduced by law, the marginal product of labour will increase. If people make substitution towards land, that means they now use relatively more land, so the marginal product of land will decrease. (只是比例上多了用地, 不是實際上多了用地)