Question

J. Batts​ & Co.​ (JBC) is a small business that is both a monopolist and a monopsonist. It produces bat traps using a rare mineral. JBC is the only producer of these traps and the only purchaser of the mineral. Demand for the​ company's traps is P​ = 104 - 2Q​, where P is the price JBC charges per trap and Q is the number of traps​ sold, in thousands of units. Supply of the rare mineral is m​ = 4 ​+ 6X​, where m is the price of one pound of the mineral and X is the amount of the mineral​ purchased, in thousands of pounds.​ JBC's production function is Q​ = 2X​, so the marginal product of X is 2.

JBC should purchase X​ =_____ thousand pounds of the mineral and pay a price of m​ = $______ per pound. ​(Enter your responses rounded to two decimal​ places.)

Answer 1

Marginal revenue product (MRP) of X must equal to the price of X for equilibrium.

Given,

Marginal product (MP) = 2

MRP = MP × P

            = 2 × P

            = 2 × (104 – 2Q)

            = 208 – 4Q

As given, Q = 2X

MRP = 208 – 4 (2X)

         = 208 – 8X

Thus, MRP must equal to m

MRP = m

208 – 8X = 4 + 6X

14X = 208 – 4

14X = 204

X = 204/14

    = 14.57 (Answer)

Now this is to be placed in the function of m

m = 4 + 6X

    = 4 + 6 × 14.57

    = 4 + 87.42

    = 91.42 (Answer)