The management of the Mini Mill Steel Company estimated the following elasticiti

Question

The management of the Mini Mill Steel Company estimated the following elasticities for a special type of steel they sell: E_p = -2, E_l = 1, and E_XY = 1.5, where X refers to steel and Y to aluminum. Next year, the firm would like to increase the price of the steel it sells by 6 percent. The management of the firm forecasted that income will rise by 4 percent next year, and the price of aluminum will fall by 2 percent. (a) If the sales of the firm this year are 1, 200 tons of the special type of steel, how many tons of steel can the firm expect to sell next year? (b) By what percentage must the firm change the price of steel to keep its sales at 1, 200 tons next year?

Explanation / Answer

a)
p   =%Q/%Px
-2   =%Q/6%
%Q=6%x (-2)
%Q   =-12%

i   =%Q/%I
1=%Q/4%
%Q   =4%

Exy=%Qx/%Py
1,5=%Q/-2%
%Q=–3%

Total Q =-12%–3%+4%=– 11%

Net change=1.200 x ( 100% – 11% ) = 1.200 x 89% = 1.068

b)
Q = X%–3%+4%

0 =X%–3%+4%

X% = – 1%
p   =%Q/   %Px  
-2   =-1%   /X%  
X=0,5%
%P   =0.5%

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