Q4. A researcher estimated that the price elasticity of demand for automobiles in the United States is -1.2, while the income elasticity of demand is 3.0. Next year U.S auto makers intend to increase the average price of automobiles by 5% and they expect the consumers’ disposable income to increase by 3%.

a)      If sales of domestically produced automobiles are 8 million this year, how many automobiles do you expect U.S auto makers to sell next year?

b)     By how much should domestic automakers increase the price of automobiles if they wish to increase sales by 5% next year?

SOLUTION

(a)

Qx’      =          Qx + Qx(dpx/px)Ep + Qx(dI/I) EI                                    

Qx’     =          8 + 8(0.05)X-1.2 + 8(0.03) x 3

Qx’     =          8 + 8(-0.06) + 8(0.09)

Qx’     =          8(1 – 0.06 + 0.09)

Qx’     =          8.24 Million

(b)                        

If we intend to increase 5% sales then sales becomes 8.4 Million, The equation becomes

8.4                   =   8+8+(dpx/px)(-1.2)+2(0.03)(3) 

                                                              

8.4                   = 8.72+(-9.6)(dpx/px)         

8.4 – 8.72       =(-9.6)(dpx/px)

    (dpx/px)          =   0.32/9.6      

        dpx/px)               =   0.0333

There should be 3.33% increase in price if company want to increase 5% sales.