Answer to Question #191633 in Accounting for mahlet

Question

Suppose that the firm operates in a perfectly competitive market. The market price of his

product is$10. The firm estimates its cost of production with the following cost function:

TC=10q-4q2+q3

Answer 1

Solution:

The firm will maximize profits at the point where:

P = MC

Where: P = Market price of the product

           MC = Marginal Cost

MC = The derivative of the total cost relative to the quantity

MC = $\frac{\partial TC} {\partial q}$ = 10 – 8q + 3q²

MC = 10 – 8q + 3q²

Market Price (P) = 10

Set P = MC

10 – 8q + 3q² = 10

3q² – 8q – 20 = 0

Solving for q, we get the following:

q = 4.239, q = -1.573

We take the positive q:

The profit maximizing level of output: q = 4.239

 

The level of profit at equilibrium will be as follows:

Profit = Revenue – TC

Revenue = $P\times Q = 10\times 4.239 = \$42.39$

Total Cost = 10q – 4q²+ q³

Substitute with quantity:

TC = 10(4.239) – 4(4.239)² + 4.239³

TC = 42.39 – 71.88 + 76.17

TC = 42.39 + 76.17 – 71.88

TC = 46.68

Profit or Loss = 42.39 – 46.68 = - $4.29

Profit or Loss = - $4.29