The table below represents the cost function of a poultry farm. The price of a crate of egg is $21. Use the information contained in the table to answer the...
Question 1 Report
The table below represents the cost function of a poultry farm. The price of a crate of egg is $21. Use the information contained in the table to answer the questions that follow.
| Quantity of eggs (in crates) | Total cost (in $) |
| 0 | 50 |
| 1 | 55 |
| 2 | 62 |
| 3 | 75 |
| 4 | 96 |
| 5 | 125 |
| 6 | 162 |
| 7 | 203 |
| 8 | 248 |
(a) What Is the fixed cost of the farm? (2 marks]
(b)(i) Calculate the marginal cost at each level of output. [9 marks]
(ii) What is the profit maximizing output of the farm? [3 marks]
(c) Draw the demand curve for the farm. [6 marks].
Answer Details
(a) Fixed cost. Fixed cost is the total cost when output is zero, because it does not vary with output. From the table, at 0 crates total cost is \$50, so fixed cost = \$50.
(b)(i) Marginal cost at each level, \( MC = TC_n - TC_{n-1} \):
| Output (crates) | Total cost ($) | MC ($) |
|---|---|---|
| 0 | 50 | - |
| 1 | 55 | \(55-50=5\) |
| 2 | 62 | \(62-55=7\) |
| 3 | 75 | \(75-62=13\) |
| 4 | 96 | \(96-75=21\) |
| 5 | 125 | \(125-96=29\) |
| 6 | 162 | \(162-125=37\) |
| 7 | 203 | \(203-162=41\) |
| 8 | 248 | \(248-203=45\) |
(b)(ii) Profit-maximising output. A firm maximises profit where marginal cost equals price (which is the marginal revenue for a price taker). The price of a crate is \$21, and \( MC = \$21 \) at an output of 4 crates. So the profit-maximising output is 4 crates: beyond this, each extra crate costs more to produce (\$29, \$37, ...) than the \$21 it earns.
(c) The demand curve. Because the price stays at \$21 no matter how much the farm sells, the farm is a price taker in a perfectly competitive market. Its demand curve is a horizontal (perfectly elastic) straight line drawn at the price level \$21 on the vertical (price) axis, running parallel to the quantity axis. This same line is the firm's average revenue and marginal revenue curve.
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