Micro 5.2-Labor Market Formulas and Proofs

Prove: MRP = DL

MRP = * [(∆TPP) / ()]  = MR * = given firms demand labor due to the revenue the worker brings to the firm.

Prove: VMP = DL (PERFECT COMPETITION PRODUCT FIRM that is hiring)

VMP = * [() / (∆ Qlabor)]  = P * = MR * MPP given P = = DL given the true value of the worker is based on the price of the product.

Prove: VMP = MRP (PERFECT COMPETITION PRODUCT FIRM that is hiring)

= P * [(∆TPP) / ( Qlabor)]  = P * MPP = MR * MPP =   given the firm is in the product market.

Prove: MRP = ∆TR / ∆ Qlabor

MRP = MR * [(∆TPP) / (∆ Qlabor)]  = [() / ()] * [(∆TPP) / (∆ Qlabor)] = [(∆TR) / (∆Qo)] * [() / (∆ Qlabor)] =

prove: MRC = wage

MRC =  [() / (∆ Qlabor)] = [(∆TRC) / ()]  =  [(w*∆ Qlabor) / (∆ Qlabor)] =  [() / (∆ Qlabor)] = given the firm is a wage-taker due to being perfectly competitive in the labor market.

Prove: MRC = SL

=  [(∆TRC) / (∆ Qlabor)] = [() / ()] =  [(∆TC) / (∆ Qlabor)] =  [(w*∆ Qlabor) / (∆ Qlabor)] = w = SL (given wage is a and a determinant of supply)