# problem set 3 demand estimation demand forecasting and production models 1

1) Consider the following scenario (adapted from Chapter 5 demand estimation question number 3, p.163):

The maker of a leading brand of low-calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:

*Q* = -5,200 â€“ 42*P* + 20*Px* + 5.2*l* + 0.20*A *+ 0.25*M*

(2.002) (17.5) (6.2) (2.5) (0.09) (0.21)

*R**2* = 0.55 *n* = 26 *F* = 4.88

Assume the following values for the independent variables:

*Q* = Quantity sold per month

*P* (in cents) = Price of the product = 500

*Px* (in cents) = Price of leading competitorâ€™s product = 600

*I* (in dollars) = Per capita income of the standard metropolitan statistical area (SMSA) in which the supermarket is located = 5,500

*A* (in dollars) = Monthly advertising expenditure = 10,000

*M* = Number of microwave ovens sold in the SMSA in which the supermarket is located = 5,000

a)Calculate the quantity using the given values for the independent variables.

b) Calculate the total revenue at this quantity.

c)What proportion of the variation in sales is explained by the independent variables?

d)Calculate the price elasticity of demand. Hint: Use the point elasticity method described on page 72. A numeric example is demonstrated in the second paragraph on that page.

e)Based on the price elasticity of demand, do you think that this firm should cut its price to increase its market share? Why or why not?

f)Compute the income elasticity.

g)Based on the income elasticity of demand, do you think that this company would be extremely concerned about the impact of a recession on its sales? Why or why not?

2) Office Enterprises (OE) produces a line of metal office file cabinets. The companyâ€™s economist, having investigated a large number of past data, has established the following equation of demand for these cabinets:

*Q* = 10,000 + 60*B* â€“ 100*P* + 50*C *where

*Q* = Annual number of cabinets sold

*B* = Index of nonresidential construction

*P* = Average price per cabinet charged by OE

*C* = Average price per cabinet charged by OEâ€™s closest competitor

It is expected that next yearâ€™s nonresidential construction index will stand at 160, OEâ€™s average price will be $40, and the competitorâ€™s average price will be $35.

a) Forecast annual sales.

b) What will be the new sales forecast if the competitor lowers its price to $32?

c) What will be the new sales forecast if OE reacts to the decrease mentioned in the previous question by lowering its price to $37? (The competitorâ€™s price will now be $32 and the firmâ€™s own price will be $37.)

d) If the index forecast was wrong, and it turns out to be only 140 next year, what will be OEâ€™s projected sales assuming the original price information of P = $40 and C = $35?

3)The Ocean Pacific fleet has just decided to use a pole-and-line method of fishing instead of gill netting to catch tuna due to a concern for endangered species that can become caught in fishing nets.

Ocean Pacific is limited in the short run to the current fleet of boats, and has decided to conduct a series of experiments to determine the impact of changing the crew size. The results of these experiments follow.

Number of Fishermen |
Daily Tuna Catch (lb) |

0 |
0 |

1 |
50 |

2 |
110 |

3 |
200 |

4 |
350 |

5 |
490 |

6 |
565 |

7 |
600 |

8 |
625 |

9 |
610 |

a) At what point (what number of fishermen) does diminishing returns occur?

b) Suppose the market price of tuna is $3.50/pound. How many fishermen should the company use if the daily wage rate is $100? (*Hint:* *Calculate MRP for each fisherman at $3.50*.)

c) Suppose a glut in the market for tuna causes the price to fall to $2.75/pound. At this new price, how many fishermen should the company now use if the daily wage rate remains at $100?

d) Suppose the price of tuna rises to $5.00/pound. At this new price, how many fishermen should the company now use if the daily wage rate remains at $100?

e) In the long run, Ocean Pacific could acquire more boats or sell some of their existing boats. What factors might influence the decision whether to acquire boats, sell boats, or remain at the current number of boats? Explain.