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aggregate supply curve

I'm having trouble working through this problems. I have the solutions to use a check values but, don't understand the process used to arrive at those values. Could you please explain step by step. Thanks!


The Potash Corporation of Saskatchewan (PCS) and two small producers supply a particular fertilizer market. The small producers behave as competitive price takers; PCS as a price leader. The marginal cost curves of the small producers are, respectively:
MC1 = 3 + 0.1q1
MC2 = 3 + 0.2q2
The marginal cost of PCS is:
MCS = 2 + 0.04qS
The market demand for fertilizer is:
Q = 80 - 10p.
(a) What is the aggregate supply curve for the small producers?
(b) What is the residual demand curve facing PCS?
(c) What is the profit maximizing level of PCS production?
(d) What price will PCS establish?
(e) What will be the quantity supplied by each of the two small producers?

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Solution Summary

The aggregate supply curve is assessed.