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Suppose Sarah owns a small company that makes wedding cakes
Suppose Sarah owns a small company that makes wedding cakes. The table below shows how Sarah's total cost varies depending on the number of wedding cakes she makes each day. The baker business is competitive.
| Number of Cakes Per Day | Total Cost Per Day ($) |
|---|---|
| 0 | 100 |
| 1 | 180 |
| 2 | 220 |
| 3 | 300 |
| 4 | 400 |
| 5 | 520 |
| 6 | 660 |
A. Compute average fixed costs, average variable costs, and the marginal cost of Sarah's bakery.
B. If each cake sells for $125, compute Sarah's profit/loss.
C. If Sarah's fixed costs go up by $200, in the short run, should she continue production or should she close her bakery? Why?
Expert Solution
Given:
- The fixed cost is incurred before the production activities commence and will be $100 at the production levels in the short run.
- Total variable cost at each level of cakes = Total cost at each level of cakes produced - Total fixed cost at each level of cakes produced
A. The table containing the average fixed costs, average variable costs, and the marginal cost of Sarah's bakery is prepared below.
| Number of Cakes Per Day (a) | Total Cost Per Day ($)(b) | Total Fixed Cost (c) | Total Variable cost (d = b - a) | Average fixed cost (c/a) | Average variable cost (d/a) | Marginal cost |
|---|---|---|---|---|---|---|
| 0 | $100.00 | $100.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| 1 | $180.00 | $100.00 | $80.00 | $100.00 | $80.00 | $80.00 |
| 2 | $220.00 | $100.00 | $120.00 | $50.00 | $60.00 | $40.00 |
| 3 | $300.00 | $100.00 | $200.00 | $33.33 | $66.67 | $80.00 |
| 4 | $400.00 | $100.00 | $300.00 | $25.00 | $75.00 | $100.00 |
| 5 | $520.00 | $100.00 | $420.00 | $20.00 | $84.00 | $120.00 |
| 6 | $660.00 | $100.00 | $560.00 | $16.67 | $93.33 | $140.00 |
B) The profit/(loss) at each level of cakes sold are prepared below
| Number of Cakes Per Day (a) | price per cake (b) | Total Revenue (c = a * b) | Total Cost (d) | profit/(loss) (c - d) | Marginal revenue | Marginal Cost |
|---|---|---|---|---|---|---|
| 0 | $125 | $0 | $100 | -$100 | ||
| 1 | $125 | $125 | $180 | -$55 | $125 | $80 |
| 2 | $125 | $250 | $220 | $30 | $125 | $40 |
| 3 | $125 | $375 | $300 | $75 | $125 | $80 |
| 4 | $125 | $500 | $400 | $100 | $125 | $100 |
| 5 | $125 | $625 | $520 | $105 | $125 | $120 |
| 6 | $125 | $750 | $660 | $90 | $125 | $140 |
C) Sarah is operating in a perfectly competitive market as the selling price remains the same at all levels. The marginal revenue is $125 per unit and is higher than the average variable cost until the supply is 5 cakes per day, indicating the revenue earned per unit is recovering the total variable cost and portion of fixed cost. In the short run, Sarah will operate and supply up to 5 cakes per day.
Profit:
The income statement is prepared at the end of the period (monthly, quarterly, half-yearly, and yearly) showing the revenues earned and expenses incurred. The profit is the amount leftover from revenue after deducting all expenses.
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