Suppose the short-run production function is q = 10 * L. If the wage rate is $10

Question

Suppose the short-run production function is q = 10 * L. If the wage rate is $10 per unit of labor, then MC=
A) q.
B) q/10.
C) 10/q.
D) 1. -< Answer

Can you please explain how to get this. I dont understand how to arrive at this number. I need to know if numbers change.

Explanation / Answer

MC = d(TC)/dQ -> Marginal cost is rate of change of total cost TC with respect to output Q TC = TVC + TFC -> Total cost = Total variable cost + total fixed cost d(TC)/dQ = d(TVC+TFC)/dQ = d(TVC)/dQ + d(TFC)/dQ since this is short run, we assume that fixed costs are constant, hence d(TFC)/dQ = 0 Hence, d(TC)/dQ = d(TVC)/dQ + 0 = d(TVC)/dQ. We get the identity that in the SR, MC = d(TVC)/dQ. In SR, again, we assume only variable input is labour and firms can hire at wage W, in this case W = 10 So we have TVC = W*L where L is total labour hired. d(TVC)/dQ = d(W*L)/dQ = W(d(L)/dQ), because W is a constant. dQ/dL is our MPL, the marginal productivity of labour, so dL/dQ = 1/MPL. Hence we have the identity that in SR, MC = W/MPL. dQ/dL here is clearly d(10*L)/dL = 10. So MC = 10/10 = 1

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