Question #55087

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

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

Expert's answer

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

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

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