Differentiation. Purpose- to determine instantaneous rate of change Eg: instantaneous rate of change in total cost per unit of the good We will learn Marginal Demand, Marginal Revenue, Marginal Cost, and Marginal Profit. Marginal Cost : MC(q). What is Marginal cost?
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Eg: instantaneous rate of change in total cost per unit of the good
We will learn
The cost per unit at a given level of production
Recall Dinner problem
C(q) = C0 + VC(q).
MC(q)- the marginal cost at q dinners
MC(100)- gives us the marginal cost at 100 dinners
This means the cost per unit at 100 dinners
How to find MC(q) ? We will learn 3 plans
In terms of money, the marginal cost at the production level of 500, $6.71 per unit
D(q) is always decreasing
All the difference quotients for marginal demand are negative
MD(q) is always negative
If (c is a constant) then
If (m is a constant) then
- In project,
- units are
Marginal Revenue in dollars per drive
- In project,
- units are
- Marginal Cost is given in original data
- Cost per unit at different production levels
- Use IF function in Excel
MP(q) = MR(q) – MC(q)
- If MP(q) > 0, profit is increasing
- If MR(q) > MC(q), profit is increasing
- If MP(q) < 0, profit is decreasing
- If MR(q) < MC(q), profit is decreasing
- Calculate MC(q)
Nested If function, the if function using values for Q1-4 & 6
In the GOLDEN sheet need to use cell referencing for IF function because we will make copies of it, and do other project questions
$ 72 per drive
- Maximum profit occurs when MP(q) = 0
- Max profit occurs when MR(q) = MC(q)
- Estimate quantity from graph of Profit
- Estimate quantity from graph of Marginal Profit
1. What price? $285.88
2. What quantity? 1262(K’s) units
3. What profit? $42.17 million
- Create one graph showing MR and MC
- Create one graph showing MP
- Prepare computational cells answering your team’s questions 1- 3
1. What price should Card Tech put on the drives, in order to achieve the maximum profit?
2. How many drives might they expect to sell at the optimal price?
3. What maximum profit can be expected from sales of the 12-GB?
4. How sensitive is profit to changes from the optimal quantity of drives, as found in Question 2?
5. What is the consumer surplus if profit is maximized?
6. What profit could Card Tech expect, if they price the drives at $299.99?
7. How much should Card Tech pay for an advertising campaign that would increase demand for the 12-GB drives by 10% at all price levels?
8. How would the 10% increase in demand effect the optimal price of the drives?
9. Would it be wise for Card Tech to put $15,000,000 into training and streamlining which would reduce the variable production costs by 7% for the coming year?