MetLife Inc.PLF Software

Danny Gruen

PLF (Personal Learning Finance)

Programmed in SQL

Specific for PC◦ Mac coming soon...

Background Information

Product:◦ PLF – Program for end-user to analyze and predict

personal financial decisions Objectives

◦ Maximize profit◦ Use market data to create demand, revenue, cost

and profit functions ◦ Use the functions to find the optimal price at which

to produce and sell and at the maximum profit ◦ See how changes in cost, price, and demand affect

profit

Product & Objectives

Demand is a quadratic function

Our market data given is accurate

Our product is in a monopoly market

Assumptions

Demand◦ D(q) : price per unit (dependent on q)◦ q: number of units sold

Revenue◦ R(q): quantity multiplied by price per unit◦ R(q) = q x D(q)

Cost◦ C(q): comprised of two components → fixed cost

(constant) and variable cost (dependent on q)◦ C(q) = Fixed Cost + VC(q)

Profit◦ P(q): revenue minus total cost◦ P(q) = R(q) – C(q)

Definitions & Terms

Marginal Profit◦MP(q): Profit generated from extra unit sold; MP(q) = MR(q) – MC(q)

Marginal Cost◦MC(q) = Cost incurred for producing the extra unit; MC(q) = C’(q)

Marginal Revenue◦MR(q): The revenue generated from one extra unit sold

◦MR(q) = R’(q)

Definitions & Terms

Market Data

Demand

- Our demand graph is a graphical representation of the quadratic demand function through plotting the market data points

K’s

Revenue

•R(q) = D(q) x q

•R(q) =-.0002605115x3-.0503324462x2+568.7833351581x

•Peak of graph is Max Revenue

Marginal Revenue

Derivative of Revenue graph

•Where graph crosses x-axis this is our max revenue

Cost C(q)

The cost graph depicts the sum of the fixed and variable costs at different quantities or levels of production

Cost Function: C(q) = Fixed cost +variable cost

13848001670124.8005001420155.5000850270.

)(qqqqqq

qC

Marginal Cost

•Derivative of Cost function

Revenue Cost and Profit

•The points where the two graphs meet are the break even points, where the profit = 0, and when revenue = cost

•The maximum profit is represented by the greatest distance between the revenue and cost

Profit P(q)

P(q) = R(q) – C(q); MP(q) = MR(q) – MC(q) The profit graphs shows the relationship between the number

of units sold and the profit earned at these various quantities The maximum profit is $34.30 million at 666,000 procedures.

Marginal Profit

Where the graph crosses the x-axis is where we

achieve max profit

Marginal Data

Max Profit occurs where MC(q) = MR(q)

MR(q) = MC(q) at q=666

What is the optimal price to set our product at?◦ We determined that our optimal price would be

$419.68 How many pills can we sell at this price?

◦ We determined that we could sell 666,000 pills What is the maximum profit?

◦ Maximum profit = $34.30 million

Maximizing Profit

We must find the revenue at the profit maximizing point:◦ R(q) = optimal price x expected quantity sold at

maximum price= $419.68 x 666= $279.54 million

Subtract total possible revenue from the revenue at profit maximizing point:

◦ Consumer Surplus:

Consumer Surplus

)666*419(78333.56805033.00026..666

0

2 dxxx

=195548725.06

Profit Sensitivity

A 1% decrease in demand yields:•Optimal price of $419.20•Quantity of 961.06??•Profit would decrease by $10 thousand•Total profit of $34.29 million

A 2% increase in marginal cost yields:

Optimal price of $419.68Quantity of 666 thousandDecreased the profit by $7.03 million

total profit of $25.99 million

Profit Sensitivity

Further Analysis

The EndQuestions?