Fukaku Footwear wished to estimate the demand function for its ‘Elite VS600’ women’s shoes. The company’s economist believed that the main determinants of ‘Elite VS600’ shoes are: i) ii) iii) iv) the price of the shoes (Px) the price of a competitor’s shoes Dr. Martin (Py) the price of another competitor’s shoes ‘Madame69’ (Pz) and disposable per capita income (Y)

A regression was run by using SPSS package and the result is shown as follows: LS//Dependent Variable is Qx Variable Coefficient C 250.7 Px -410.3 Py 240.3 Pz 180.3 Y 1.23 R-Squared = 0.857 S.E of regression = 265.6 Qx represents quantity (pairs) demanded per month. The current values of the dependent variables are Px = $80, Py = $75, Pz $82.5 and Y = $5250 a) Calculate the price and income elasticities of demand for ‘Elite VS600’ shoes. What do these values mean?

Standard Error -150.3 180.5 70.4 0.23

t-statistic 2.73 1.33 2.56 5.36

Find Qx; Qx = C – Px + Py + Pz + Y = 250.7 – 410.3Px + 240.3Py + 180.3Pz + 1.23Y = 250.7 – 410.3(80) + 240.3(75) + 180.3(82.5) + 1.23(5250) = 6781.45

i)

= -4.84 (elastic) ii) = 0.952 (necessity goods)

b) Derive the equation of the demand curve and write it in the conventional way.

Qx Px

= 250.7 – 410.3Px + 240.3(75) + 180.3(82.5) + 1.23(5250) = 39605.45 – 410.3Px = 96.528 – 0.00244Qx

c)

Suppose that the marginal cost of Elite VS600 is constant at $50, what is the profit maximizing price and output?

» MC = MR Given MC = 50 Find MR = TR =PxQ = (96.528 – 0.00244Qx) x Qx = 96.528Qx – 0.00244Qx2 = 96.528 – 0.00488Qx » MC = MR = 50 96.528 – 0.00488Qx = 50 Qx = 9534.43 → (i) Put (i) into Px demand curve, Px = 96.528 – 0.00244 (9534.43) = 73.26

d) At the profit maximizing price, what range of sales volume can be expected at 95% confidence limits?

MR =

At max TR; Px = 73.26 Qx = 9534.43 Given SEE = 265.6 t interval value (Rule of Thumb) = 2 SEE = Q + t-value (SEE) = (+) 9534.43 + 2 (265.6) = 10065.63 = (-) 9534.43 - 2 (265.6) =