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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 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.

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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