Document Sample

Demand, Revenue, Cost, & Profit Demand Function – D(q) • p =D(q) • In this function the input is q and output p • q-independent variable/p-dependent variable [Recall y=f(x)] • p =D(q) the price at which q units of the good can be sold • Unit price-p • Most demand functions- Quadratic [ PROJECT 1] • Demand curve, which is the graph of D(q), is generally downward sloping – Why? Demand Function – D(q) • As quantity goes down, what happens to price? -price per unit increases • As quantity goes up, what happens to price? -price per unit decreases Example Demand Function y = -0.0000018x2 - 0.0002953x + 30.19 $32 $24 D(q) $16 $8 $0 0 1,000 2,000 3,000 4,000 q Define the demand function to be D(q) = aq2 + bq + c, where a = 0.0000018, b = 0.0002953, and c = 30.19. Example problem( Dinner.xls) • Restaurant wants to introduce a new buffalo steak dinner • Test prices (Note these are unit prices) Price $14.95 $19.95 $24.95 $29.95 Number sold per week 2,800 2,300 1,600 300 • If I want the demand function, what is our input/output? • Recall p=D(q) Revenue Function – R(q) • R(q)=q*D(q) • The amount that a producer receives from the sale of q units • Recall p=D(q) • What is p? -unit price per item • Revenue= number of units*unit price Example Revenue Function $50,000 $40,000 $30,000 R(q) $20,000 $10,000 $0 0 1000 2000 3000 4000 q Sample Data Points q D(q) R(q) 0 $30.19 $0.00 8 $30.19 $241.50 16 $30.18 $482.96 24 $30.18 $724.37 32 $30.18 $965.72 40 $30.18 $1,207.01 Cost Function A producer’s total cost function, C(q), for the production of q units is given by C(q) = C0 + VC(q) =fixed cost + variable cost [here VC(q)-variable cost for q units of a good] = 9000+177*q0.633 • Recall:fixed cost do not depend upon the amount of a good that is produced Example Fixed Cost C0 $9,000.00 Variable Costs Number of Dinners(q) Cost-VC(q) 1,000 $14,000.00 2,000 $22,000.00 3,000 $28,000.00 Variable cost function • Assume that we are going to fit a power function • VC(q) = u * qv (here u and v are constants) Variable Costs Function 0.633 y = 177x $50,000 $40,000 VC(q) $30,000 $20,000 $10,000 $0 0 1,000 2,000 3,000 4,000 q Cost function Recall C(q) = C0 + VC(q). q C(q) 0 $9,000.00 = 9000+177*q0.633 8 $9,660.13 16 $10,023.72 Cost Function 24 $10,323.27 32 $10,587.57 $50,000 $40,000 40 $10,828.43 C(q) $30,000 $20,000 $10,000 $0 0 1000 2000 3000 4000 q Profit Function • let P(q) be the profit obtained from producing and selling q units of a good at the price D(q). • Profit = Revenue Cost • P(q) = R(q) C(q) Profit=Revenue-Cost Sample Data Points q C(q) R(q) P(q) 0 $9,000.00 $0.00 -$9,000.00 8 $9,660.13 $241.50 -$9,418.63 16 $10,023.72 $482.96 -$9,540.76 24 $10,323.27 $724.37 -$9,598.90 32 $10,587.57 $965.72 -$9,621.85 40 $10,828.43 $1,207.01 -$9,621.41 Profit Function-Dinner problem Profit Function $15,000 $10,000 $5,000 P(q) $0 -$5,000 0 1000 2000 3000 4000 -$10,000 q Summary –Dinner Problem Revenue and Cost Function Cost Revenue $50,000 $40,000 Dollars $30,000 $20,000 $10,000 $0 0 1000 2000 3000 4000 q Profit Function $15,000 $10,000 $5,000 P(q) $0 0 1000 2000 3000 4000 -$5,000 -$10,000 q Project Focus • How can demand, revenue,cost, and profit functions help us price T/2 Mega drives? • Must find the demand, revenue and cost functions Important – Conventions for units • Prices for individual drives are given in dollars. • Revenues from sales in the national market are given in millions of dollars. • Quantities of drives in the test markets are actual numbers of drives. • Quantities of drives in the national market are given in thousands of drives. Projected yearly sales – -National market • We have the information about the Test markets & Potential national market size [test market 1 sales] national sales( K ' s ) for test market 1 size of national market ( K ' s ) [ size of test market 1] • Show marketing data.xls (How to calculate) Demand function-Project1 D(q) • D(q) –gives the price, in dollars per drive at q thousand drives • Assumption – Demand function is Quadratic • The data points for national sales are plotted and fitted with a second degree polynomial trend line • Coefficients- 8 decimal places Demand Function (continued) Demand Data $500 $400 2 y = -0.00005349x - 0.03440302x + 414.53444491 Price $300 $200 $100 $0 0 400 800 1,200 1,600 2,000 2,400 2,800 Quantity (K's) D(q) =-0.00005349q2 + -0.03440302q + 414.53444491 Marketing Project Revenue function- Project1 R(q) • R(q) is to give the revenue, in millions of dollars from selling q thousand drives • Recall D(q)- gives the price, in dollars per drive at q thousand drives • Recall q – quantities of drives in the national market are given in thousand of drives Revenue function-R(q) • Revenue in dollars= D(q)*q*1000 • Revenue in millions of dollars = D(q)*q*1000/1000000 = D(q)*q/1000 • Why do this conversion? Revenue should be in millions of dollars Revenue function Revenue Function $500 $400 R (q ) (M's) $300 $200 $100 $0 0 400 800 1,200 1,600 2,000 2,400 2,800 q (K's) Total cost function-C(q) • C(q)-Cost, in millions of dollars,of producing q thousand drives Fixed Cost Variable Costs (M's) (M's) $135.0 Batch Size (K's) Marginal Cost 1 First 800 $160.00 2 Second 400 $128.00 3 Further $72.00 Total cost function-C(q) • Depends upon 7 numbers – q(quantity) – Fixed cost – Batch size 1 – Batch size 2 – Marginal cost 1 – Marginal cost 2 – Marginal cost 3 Cost Function The cost function, C(q), gives the relationship between total cost and quantity produced. 160q 135 if 0 q 800 1,000 128( q 800 ) C( q ) 263 if 800 q 1,200 1,000 314.2 72( q 1,200 ) if q 1,200 1,000 User defined function COST in Excel. Marketing Project How to do the C(q) in Excel • We are going to use the COST function(user defined function) • All teams must transfer the cost function from Marketing Focus.xls to their project1 excel file • Importing the COST function(see class webpage) Revenue & Cost Functions Revenue & Cost Functions $500 $400 Revenue $300 (M's) Cost $200 $100 $0 0 400 800 1,200 1,600 2,000 2,400 2,800 q (K's) Main Focus-Profit • Recall P(q)-the profit, in millions of dollars from selling q thousand drives • P(q)=R(q)-C(q) Profit Function The profit function, P(q), gives the relationship between the profit and quantity produced and sold. P(q) = R(q) – C(q) Profit Function $70 $60 $50 P (q ) (M's) $40 $30 $20 $10 $0 -$10 0 400 800 1,200 1,600 2,000 -$20 q (K's) Rough estimates based on Graphs of D(q), P(q) • Optimal Quantity- Profit Function $70 $60 $50 1200 P (q ) (M's) $40 $30 $20 • Optimal Price- $10 $0 -$10 0 400 800 1,200 1,600 2,000 -$20 $300 q (K's) • Optimal Profit- Demand Data $42M $500 $400 2 y = -0.00005349x - 0.03440302x + 414.53444491 Price $300 $200 $100 $0 0 400 800 1,200 1,600 2,000 2,400 2,800 Quantity (K's) Goals • 1. What price should Storage 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 T/2 Mega? • 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? 32 Goals-Contd. • 6. What profit could Storage Tech expect, if they price the drives at $299.99? • 7. How much should Storage Tech pay for an advertising campaign that would increase demand for the T/2 Mega 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 Storage Tech to put $15,000,000 into training and streamlining which would reduce the variable production costs by 7% for the coming year? 33 What’s next? • So far we have graphical estimates for some of our project questions(Q1-3 only) • We need now is some way to replace graphical estimates with more precise computations

DOCUMENT INFO

OTHER DOCS BY malj

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.