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a. Assume that the market price is established by the following equations: Supply Curve: P = 10 - 2Q + 0.15Q2 Demand Curve: P = 14.6 - 0.8Q Where P is price and Q is Quantity of output of a particul…

a. Assume that the market price is established by the following equations:
Supply Curve: P = 10 - 2Q + 0.15Q2
Demand Curve: P = 14.6 - 0.8Q

Where P is price and Q is Quantity of output of a particular commodity.
Assume also that a particular firm is operating under perfect competition and that its cost and revenue functions are:

TC = 10Q – Q2 + 0.05Q3
TR = PQ

Where TC is total cost, TR is total revenue and P is price.

i. Find the market price for this commodity in question.
ii. Draw the total cost and total revenue curves of the firm and find the
quantity of output which maximises profit. Confirm your findings
mathematically.
iii. Derive a total profit equation and draw a total profit curve. Show
mathematically that total profit reaches a peak when MC=MR.
iv. Draw the average and marginal cost curves and the average and
marginal revenue curves of the firm and find the quantity of output
which maximises profit.
vi. Briefly explain the equilibrium price and quantities of the firm and of
the market.

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