Minimum Wage?

Question

Suppose a government decides to enact a minimum wage law such that firms are required to pay a minimum wage w. Demonstrate that in a competitive equilibrium,
the representative consumer can be no better off and may be, in fact, worse off.

Answer 1

Assume consumers are labor and capital returns are reinvested in most profitable industry.
production function Q(K,L) and cost =rK+wL
competitive firm will maximize profit pQ-rK-wL
so p dQ/dK-r=0 and p dQ/dL-w=0
the marginal product of capital =r/p
the marginal product of labor =w/p
If all industries are equally capital intensive production will be unchanged and price will increase so w/p and r/p will be unchanged
If not then show that when production and prices will shift between industries to equalize profits and the result will less advantageous to consumers(workers). That is they will have less utility because you have shifted away from Pareto optimal production/consumption.

Answer 2

1. Draw your S and D curves such that an equilibrium exists.
2. Draw another graph with a demand curve and the price > greater than the equilibrium price.

3. compare the consumer surpluses

Answer 3

Minimum wage is well intended, but it tends to hurt those at the lowest end of the social ladder:

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