Micro_Handout3.html

Intro to Micro 3: Firms
Optimal Choices

Logic of Business Choices

Two Examples

RIU
Tutoring

Two Approaches

Tables
Graphs

Major Divisions of Analysis (Outline)

Revenue and Demand
Revenue Relationships
- Total Revenue
- Average Revenue (and price)
- Marginal Revenue
  - and elasticity
Output and Pricing Decisions and Input Choices
- MR = MC

Example 1: Tutoring - The Tabular Approach

Revenue and Demand
R = P*Q

Revenue Relationships

Demand and Revenue

Grade (Q)	Price (P)	Total Revenue (TR)	Average Revenue (AR)	Marginal Revenue (MR)
10	$10	$100	$10
22	$9	$198	$9	$8.17
36	$8	$288	$8	$6 .43
46	$7	$322	$7	$3.40
54	$6	$324	$6	$0.25
60	$5	$300	$5	$-4.00

Total revenue is derived by multiplying the two columns (R = P*Q).
Average revenue, or revenue per unit of output, is derived by taking total revenue and dividing it by output (Ex. AR @ 46 units of output equals $322/46 = $7).
Marginal revenue, the change in revenue generated by a one unit change in output, appears in the final column. For example, when the decision is made to increase output (grades) from 36 to 46, revenue increases from $288 to $322. In this case we would compute the marginal revenue of the 46 unit of output as (MR = ($322-$288)/(46-36) = $34/10 = $3.40).

Output and Pricing Decisions

Revenue, Cost, and Profit

Quantity	Price	Total Revenue	Average Revenue	Marginal Revenue	Total Cost	Marginal Cost	Total Profit	Marginal Profit
10	10	100	10		8		92
22	9	198	9	8.17	13	.42	185	7.75
36	8	288	8	6.43	18	.36	270	6.07
46	7	322	7	3.40	23	.5	299	2.9
54	6	324	6	0.25	28	.63	296	-.38
60	5	300	5	-4.00	33	.83	267	-4.83

Total Profit: total revenue - total cost

Marginal Profit: additional profit obtained by producing and selling 1 more unit of output. Marginal profit =marginal revenue - marginal cost. If marginal profit is positive it tells us that the decision to expand production will increase revenue more than costs and thus a profit seeking firm should continue to expand production.

Logic of Profit Maximization: implications of decision to raise output
1. Profit = Revenue - Cost
2. Revenue = depends on demand
3. Cost = depends on input use and costs
4. Marginal revenue (MR) is the additional revenue of the decision
5. Marginal Cost (MC) is the additional cost of the decision
6. Marginal Profit (MP) = MR - MC
7. MP > 0 means that the decision will increase profit
8. MP > 0 means that MR > MC
9. MR = MC - the maximum profit choice
10. Since FC does not affect MC, then FC does not affect optimal choice

Example 1: Tutoring - The Graphical Approach

The Concepts

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Total Revenue

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Average Revenue

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Marginal Revenue

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The Rules

Approach #1: Total Revenue and Cost

Maximum profit occurs when the vertical distance between the curves is greatest

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Approach #2: Marginal Revenue and Marginal Cost

Maximum profit occurs when the two curves intersect. At that level of output MR = MC. When the MR curve is above the MC curve, you have MR > MC so the firm should expand output.

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Approach #3: Total Profit

Maximum profit occurs when the Profit curve reaches its maximum. This is the same point where the gap between revenue and cost is largest in the first diagram.

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Approach #4: Marginal Profit

Maximum profit occurs when the curve crosses the axes (when it equals 0). Since marginal profit is defined as MR - MC, then it is just the difference between the MR and MC graphs. If marginal profit is positive, then MR > MC and the firm should continue to expand. It will do so as long as marginal profit is > 0.

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Example 2: RIU - The Tabular Approach

The Concepts and Rules

The University's Finances: Revenue, Cost, and Profit

Students	Tuition	Total Revenue	Marginal Revenue	Total Cost	Average Cost	Marginal Cost	Total Profit	Marginal Profit
6700	10.2	68340		45000	6.72		23340
7300	10.1	73730	8.98	48500	6.64	5.83	25230	3.15
8000	10	80000	8.96	52000	6.50	5.00	28000	3.96
8775	9.9	86873	8.87	55500	6.32	4.52	31373	4.35
9800	9.8	96040	8.94	59000	6.02	3.41	37040	5.53
10125	9.7	98213	6.68	62500	6.17	10.77	35713	-4.08
10400	9.6	99840	5.92	66000	6.35	12.73	33840	-6.81
10625	9.5	100938	4.88	69500	6.54	15.56	31438	-10.68

Examples of some calculations:

$9.9 = at a tuition rate of $9,900, RIU will have 8,775 students
$80,000 = $80,000,000 total revenue when there are 8,000 students paying tuition of $10,000 each
$8.94 = $8,940 = marginal revenue of moving from 8775 to 9800 students = Drevenue/Doutput = ($96,040-$86,873)/(9800-8775) = (9,167/1025) = 8.94
$55,000 = $55,000,000 total cost of a university with 8775 students
$6.32 = $6,320 = average cost = cost per student of a university with 8,775 students = $55,500/8775 = $6.32
$4.52 = $4,520 = marginal cost of moving from 8000 to 8775 students = ($55,500-$52,000)/(8775-8000) = (3500/775) = $4.52
$35,713 = $35,713,000 total profit at 10,125 student = total revenue-total cost
$5.53 = $5,530 = marginal profit = (marginal revenue - marginal cost) = ($8.94 - $3.41) = $5.53

Example 2: RIU - The Graphical Approach

Total Cost, Revenue, and Profit

Marginal and Average Revenues, Costs, and Profit

Bottom Line: Any firm that wants to maximize profit should choose an output level - or a price for their product - in such a way that the follow the Optimal Choice Rule

Marginal Revenue = Marginal Cost

* in this example we would continue to expand as long as marginal revenue > marginal cost since this would mean profit would be increasing (revenue rising more than costs). In this simple example we would stop expanding the size of the school at 9800 students (when you look at the marginal analysis you see that it is at a size greater than 9,800 and less than 10,125)