Let the Demand and Supply for Two Linked Products, Say $Q _ { c } { } ^ { d } = 12$

Let the demand and supply for two linked products, say corn and soy, be the following: $Q _ { c } { } ^ { d } = 12$ $- 2 p _ { c } + p _ { s } ; Q _ { c } { } ^ { s } = 4 + p _ { c } ; Q _ { s } ^ { d } = 6 - 4 p _ { s } + p _ { c } ; Q _ { c } { } ^ { s } = 4 + p _ { s }$ . The superscript refers to "demand" (d) or "supply" (s) and the subscript refers to corn (c) or soy (s) . Now, suppose that the demand for corn shifts to $Q _ { c } { } ^ { d } = 18 - 2 p _ { c } + p _ { s }$ . If the price of soy is free to adjust in response to this shift, what are the new equilibrium prices of corn and soy?

A) $p _ { c } = 5.14 ; p _ { s } = 1.43$
B) $p _ { c } = 6.20 ; p _ { s } = 2.15$
C) $p _ { c } = 2.50 ; p _ { s } = 2.50$
D) $p _ { c } = 4.35 ; p _ { s } = 2.00$