Firm X Produces Output $x$ And Firm Y Produces Outputyusing Capital $K$

Multiple Choice

Firm X produces output $x$ and Firm Y produces outputyusing capital, $K$ , and labor, $L$ , as inputs. Firm X has marginal rate of technical substitution $M R T S ^ { x } { } _ { K } L = K _ { x } / L _ { x _ { 0 } }$ , while firm $Y$ has marginal rate of technical substitution $M R T S _ { K , L } = 9 K _ { y } / L _ { y }$ . Which of the following allocations satisfies input efficiency?

A) Firm X has 5 units of $K$ and 3 units of $L$ , and Firm Y has 3 units of $K$ and 1 unit of $L$ .
B) Firm X has 5 units of $K$ and 5 units of $L$ , and Firm Y has 1 unit of $K$ and 9 units of $L$ .
C) Firm X has 9 units of $K$ and 1 units of $L$ , and Firm Y has 5 units of $K$ and 5 units of $L$ .
D) Firm X has 5 units of $K$ and 5 units of $L$ , and Firm Y has 1 unit of $K$ and 3 units of $L$ .