4. Shoes For Less (SFL) hires you to determine the demand for their shoes, and y

Question

4. Shoes For Less (SFL) hires you to determine the demand for their shoes, and you estimate this to be:

Qd = 32,000 - 1200P + 600Pc + 1.2Y + 0.06A

where the independent variables are respectively: price of SFL's shoes, price of competitors' shoes, per capita income (in $) and advertising (in $) by SFL. You observe that competitors have, on average, priced their shoes at $40, while SFL charges $35. Per capita income level in the store's geographic market averages $25,000. SLF's advertising expenditure is $550,000 per month.

i) Explain clearly to your client what each of the coefficients means.

ii) Should SFL expand to wealthier areas?

iii) What should SFL do to maximize revenue?

iv)Should SFL increase its advertising expenditure?

v) A prior consultant had originally estimated the demand for SFL's shoes, and obtained:

Qd = 50,000 - 500P + 100Pc + 0.1Y

Explain the difference in the results between your results and those of the original consultant.

Explanation / Answer

Qd = 32,000 - 1,200P + 600Pc + 1.2Y + 0.06A

(i)

The coefficient of P signifies that as price of SFL shoes rise (fall) by $1, its quantity demanded will fall (rise) by 1,200 units.

The coefficient of Pc signifies that as price of SFL shoes' competitiors rise (fall) by $1, its demand will rise (fall) by 600 units.

The coefficient of Y signifies that as consumer income rise (fall) by $1, its demand will rise (fall) by 1.2 units.

The coefficient of A signifies that as advertise expenditure rise (fall) by $1, its demand will rise (fall) by 0.06 units.

(ii)

In wealthier areas, consumer income (Y) is higher. Since coefficient of Y is positive, higher income will increase demand for SFL, therefore it should expand in wealthier areas.

(iii)

Plugging in given values,

Qd = 32,000 - 1,200P + 600 x 40 + 1.2 x 25,000 + 0.06 x 550,000

Qd = 32,000 - 1,200P + 24,000 + 30,000 + 33,000

Qd = 119,000 - 1,200P

1,200P = 119,000 - Qd

P = (119,000 - Qd)/1,200

Total revenue (TR) = P x Qd = (119,000Qd - Qd2)/1,200

Revenue is maximized when dTR/dQd = 0

(119,000 - 2Qd)/1,200 = 0

119,000 - 2Qd = 0

2Qd = 119,000

Qd = 59,500

P = (119,000 - 59,500)/1,200 = 59,500/1,200 = $49.58

So to maximize reveue, SFL should charge a price of $49.58 (increase its price) and produce 59,500 units.

(iv)

Since coefficient of A is positive, higher advertising expenditure will increase the demand for SFL, therefore it should increase advertising.

NOTE: As per Answering Policy, 1st 4 parts have been answered.

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