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Interpretation of the growth rate of consumption in a simple one-good model

In Perman et al. "The efficient and optimal use of natural resources" it is presented a simple single-good model of welfare dynamic optimisation with non-renewable natural resource where: Obj: $$ max ...
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If Y=K+C, why the value of a marginal unit of capital is the same of the value of a marginal unit of output?

In a simple model of welfare dynamic optimisation with non-renewable natural resource where: $$ \dot S_t = -R_t $$ $$ \dot K_t = Q(K_t,R_t)-C_t $$ one of the first order condition is that $P_t=\...