Question

Show all your work as you go through any calculations. Thank you!

1. Suppose a firm uses labor and capital to produce boat shoes.

(a) (6 points) When presenting the optimization problem for the firm, assume that labor is put on the horizontal axis and capital on the vertical axis. If the marginal technical rate of substitution between labor and capital is currently 8 capital per worker, what does this mean? Interpret the number itself and explain fully.

(b) (4 points) By normal assumptions, what would we expect to happen to the marginal rate of technical substitution along an isoquant as labor is increased?

(c) (5 points) Explain why we expect the answer you described in part b).

Answer 1

a)labour is put on horizontal axis and Capital is put on vertical axis.

Rate of technical substitution means the rate at which labour can be substituted for capital maintaing the same level of production.

Marginal Rate of Techinical substitution being 8 capital per worker means that in order to increase one more unit of labour in Production 8 units of capital should be given up while maintaining the same level of production.

b) By normal assumption, we would expect Marginal Rate of Technical Substitution to decrease along an isoquant as labour is increased.

c) We expect the answer in b because if our normal assumption of Diminishing Marginal Product which means that as more and more factors are employed in the production(increase in labour) the additional product(Marginal Product) produced by each successive labour employed becomes smaller. This discourages the producer to lose more capital in order to increase one more unit of labour. Thus Marginal Rate of Technical Substitution decreases as we increase the labour.