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Suppose a farmer is a price taker (MR = P = 6) in soybeans with cost functions given byTC = .1q2 + 2q + 100MC = .2q + 2The firm's supply curve is given by

Question

Suppose a farmer is a price taker (MR = P = 6) in soybeans with cost functions given byTC = .1q2 + 2q + 100MC = .2q + 2The firm's supply curve is given by

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Solution

The supply curve of a firm in a perfectly competitive market is determined by the point at which the marginal cost (MC) equals the market price (P). In this case, the farmer is a price taker, meaning the price is given and constant at P = 6.

The marginal cost (MC) function is given by MC = 0.2q + 2.

To find the supply curve, we set MC = P and solve for q:

0.2q + 2 = 6 0.2q = 6 - 2 0.2q = 4 q = 4 / 0.2 q = 20

So, the supply curve for this farmer is q = 20. This means that the farmer will supply 20 units of soybeans when the market price is $6.

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