Consider a two-person (1 and 2) two good (X and Y) one-input (L) production economy.

The utility function of person 1 is given by

U₁ = 208 x₁ - 2 x₁² + y₁ - ( x₂ / 7 + x₂²)

and the utility function of person 2 is given by

U₂ = 208 x₂ - 2 x₂² + y₂

where x_i and y_i denote respectively person i's consumption amount of good X and of good Y, i=1, 2. Each person has Li = 208 units of labour, i = 1,2.

The production function of good X and that of good Y are given respectively by X = 2 L_x and Y = L_y, where L_J denotes the amount of labour used in the production of good J, J=X, Y.

Derive the production possibilities frontier equation for this economy. Then enter the value of the opportunity cost of (one more unit of) good X in terms of good Y below.