Additional Problem #2 Base Model Outcome and Evaluation
Cost Structure TC = 2.5Q2 + 10
Revenue Structure Q = 10 - .4P
Evaluation:
6. Quantity 7. Price 8. Consumer Surplus 9. Producer Surplus 10. Total Surplus 11. Dead-weight Loss
Inverse demand is P = 25 - 2.5Q
From the information provided, we have Marginal cost MC = 5Q and marginal revenue MR = 25 - 5Q
At profit maximizing output MR = MC
25 - 5Q = 5Q
Q = 25/10 = 2.5 units
Price = 25 - 2.5*2.5 = $18.75
Consumer surplus = 0.5*(Max price - price paid)*qty = 0.5*(25 - 18.75)*2.5 = 7.8125
Producer surplus = area of trapezium so formed = 0.5*(18.75 - 0 + 18.75 - 12.5)*2.5 = 31.25
Total surplus = CS + PS = 39.0625
Dead weight loss = 0.5*(price - MC)*qty = 0.5*(18.75 - 12.5)*(3.33 - 2.5) = 2.60
Additional Problem #2 Base Model Outcome and Evaluation Cost Structure TC = 2.5Q2 + 10 Revenue...
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