1 / 34

Demand, Revenue, Cost, & Profit

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

mrinal
Download Presentation

Demand, Revenue, Cost, & Profit

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Demand, Revenue, Cost, & Profit

  2. 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?

  3. 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

  4. Example Define the demand function to be D(q) = aq2 + bq + c, where a = 0.0000018, b = 0.0002953, and c = 30.19.

  5. Example problem( Dinner.xls) • Restaurant wants to introduce a new buffalo steak dinner • Test prices (Note these are unit prices) • If I want the demand function, what is our input/output? • Recall p=D(q)

  6. 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

  7. Example

  8. 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

  9. Example

  10. Variable cost function • Assume that we are going to fit a power function • VC(q) = u * qv (here u and v are constants)

  11. Cost function Recall C(q) = C0 + VC(q). = 9000+177*q0.633

  12. 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)

  13. Profit=Revenue-Cost

  14. Profit Function-Dinner problem

  15. Summary –Dinner Problem

  16. 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

  17. 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.

  18. Projected yearly sales –-National market • We have the information about the Test markets & Potential national market size • Show marketing data.xls (How to calculate)

  19. Demand function-Project1D(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

  20. Demand Function (continued) D(q) =-0.00005349q2 + -0.03440302q + 414.53444491 Marketing Project

  21. 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

  22. 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

  23. Revenue function

  24. Total cost function-C(q) • C(q)-Cost, in millions of dollars,of producing q thousand drives

  25. 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

  26. Cost Function • The cost function, C(q), gives the relationship between total cost and quantity produced. • User defined function COST in Excel. Marketing Project

  27. 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)

  28. Revenue & Cost Functions

  29. Main Focus-Profit • Recall P(q)-the profit, in millions of dollars from selling q thousand drives • P(q)=R(q)-C(q)

  30. Profit Function • The profit function, P(q), gives the relationship between the profit and quantity produced and sold. • P(q) = R(q) – C(q)

  31. Rough estimates based on Graphs of D(q), P(q) • Optimal Quantity-1200 • Optimal Price- $300 • Optimal Profit-$42M

  32. 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?

  33. 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?

  34. 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

More Related