A firm has the following short-run production output function
Q = 10L – 0.5L^2
Suppose that the output can be sold for $10 per unit. Further assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit.
a) Determine the marginal revenue function
b) Determine the value of L that maximizes profits
1) MR=dQ/dL => MR=10-L 2) MR=0 - when profit is maximum => 10-L=0 => L=10 So, Q=10*10-0.5*(10^2)=50 => TR=Q*P=50*$10=$500 TC=L*P=10*$20=$200 Profit=TR-TC=$300