BBUS 310 — PROJECT
DUE: Monday December 14, 2020
This capstone project places students in the position of a business manager making pricing decisions. You will apply the concepts learned during the course to maximize profit. Starting from the output of a multivariable regressions, you will estimate demand and cost functions, using that information to support your decision.
You are the product manager for wireless headphones and your company has the exclusive license of the product. The company’s marketing department models the demand function as Q = a + bP + cM + dPS, where Q is the annual demand for your product measured in thousands of units, P is the price of the headphones, M is the average annual family income measured in thousands of dollars, and PS is the price of the stereos with the technical specifications needed to have an excellent listening experience. The output given by Excel after running the corresponding OLS regression is the following:
DEPENDENT VARIABLE: | Q | R-SQUARE | |||
OBSERVATIONS: | 32 | 0.8270 | |||
VARIABLE | COEFFICIENT | STANDARD ERRROR | T-RATIO | P-VALUE | |
INTERCEPT | 39.1 | 10.6540 | 3.67 | 0.0019 | |
P | ̶ 0.05 | 0.0290 | -3.45 | 0.0031 | |
M | 0.06 | 0.01439 | 4.17 | 0.0006 | |
PS | ̶ 0.0225 | 0.008242 | -2.73 | 0.0144 | |
1. (10 pts.) What is the modeled demand function for headphones? Express it as a function of P, M, and PS.
Q = a + bP + cM + dPS
Q=39.1-0.05p+0.06m-0.0225ps
2. (10 pts.) Give an economic interpretation for the coefficients estimated by Excel. Are the headphones a normal or an inferior product? Is the stereo a substitute or a complement of the headphones? Justify your answer.
The cutoff value means that the smallest possible demand level is 39100.
The self-price coefficient (P) indicates that as its price rises (falls) by 1 US dollar, demand falls (rises) by 0.05 million units.
The income coefficient (M) indicates that when income increases (decreases) by $1,000, demand increases (decreases) by 0.06 million units. Since the income coefficient is positive, which means that income elasticity is positive, headphones are a normal commodity.
The stereo coefficient (Ps) means that as the price of stereo rises (falls) by $1, the demand falls (rises) by 0.0225 thousand units. Since the price coefficient of stereo speakers is negative, which means that the cross-price elasticity is positive, headphones and stereo are supplementary products.
3. (10 pts.) You hire an economic consultant to obtain estimates of income and the price of stereos next year. Her report calculates that average family income will be $45,000, and the price of a stereo $800. What will be your demand function next year? Express it as a function of P. Also, solve for the inverse demand function, that is, solve for price in terms of quantity.
m=45000
Ps=800
Q=39.1-0.05p+0.6(45000)-0.0225(800)
=39.1 – 0.05P + 2700 – 18
=2721.8-0.05p (right?)
or Q=45000+800p
4. (10 pts.) Assume that you have excess inventory and, consequently, you are just worried about maximizing revenue. What price should you charge? What would be your revenue? What is the price elasticity of demand at this price?
Q=45000-800p
MR=0
TR=P*Q=P(45000-800p)=45000p-800p^2
MR=45000-1600p=0
1600p=45000
p=28.125
Q= 45000-800(28.125)
Q=22500 units
TR=p*q=28.125*22500
TR= 632812.5
800p=45000-q
p=56.25-q/800
slope=-1/800 For every dollar that the price goes up, the firm sells 800 fewer units.
—idk bout this one ^
5. (10 pts.) Draw an accurate graph (ideally use a computer to do so) showing market demand, marginal revenue, and the area representing your total revenue.
P
Q
—this graph is editable^
6. (10 pts.) Next year, after selling the excess product, you must factor into your pricing decision the production costs. The production manager of the firm estimates (also using linear regression) that the average variable cost is given by
AVC = 326 – 12.5Q + Q2
where Q, again, is measured in thousands of units. The annual fixed cost is $270,000. Using this information express the seven types of costs (FC, VC, TC, AFC, AVC, ATC, and MC) as a function of Q. To obtain the total cost function, make sure the fixed cost is expressed in thousands of dollars before you add it to variable cost.
AFC=270000/q
FC=270000
AVC= 326-12.5Q+Q^2
VC=326q-12.5q^2+q^3
TC=FC+VC=270000+326q-12.5q^2+q^3
ATC=TC/q=270000/q+326-12.5q+q^2
MC=326-25q+3q <-(dont know bout this one)
7. (10 pts.) What price should you charge to maximize profit? How much profit would this product generate in a year? What is the price elasticity of demand at this price?
8. (10 pts.) Draw an accurate graph (ideally use a computer to do so) showing market demand (the price line), MR, ATC, AVC, MC, and the area which corresponds to your profit.
9. (10 pts.) Next year the economic consulting firm anticipates that, while income will remain relatively unchanged, the price of stereos will be $900. Would your company produce more or less headphones? How much will be your annual profit?
10. (10 pts.) Assume the price of stereos stays at $900. Would you shut down the firm in the short run, when the fixed cost cannot be recovered?
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