Question

The management of the Mini Mill Steel Company estimated the following elasticities for a special type of steel: EP 2, 1, and E where x refers to steel XY and Y to aluminum. Next year, the firm would like to increase the price of the steel it sells by 6 percent. The management forecasted that income will rise by 4 percent next year and that the price of aluminum will fall by 2 percent. (a) If the sales this year are 1,200 tons of the steel, how many tons 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?

Answer 1

Ans:

(a)Since Ep=-2, if the firm increased the price of steel by 6 percent, its sales would change by (- 2)(6%)=-12 percent. With E1=l, the forecasted increase in income of 4 percent, by itself, wouldresult in a (1) (4%)=4 percent increase in the steel sold by the firm. Finally, since Exy=1.5, areduction in the price of aluminium of 2 percent, by itself, will result in a (1.5) (-2) =-3 percentchange in steel sales. Therefore, the net effect of a 6 percent increase in the price of steel by thefiri<n, a 4 percent increase in income, and a 2 percent reduction in the price of aluminium wouldresult in a net decline in the sales of the firm of -12%+4%-3%=-11%. Thus, the steel sales of thefirm next year would be l,200-(l,200) (-11%)=1,200-132=1,068 tons.

(b) By themselves (i.e., without any increase in the price of steel), the increase in income and thereduction in the price of aluminium would result in a 1 percent increase in the steel sales of thefirm. Thus, in order to keep sales unchanged, the firm can only increase the price of steel so that, byitself, it would reduce the demand for steel by 1 percent. Since the price elasticity of demand of the steel is-2, the firm can only increase the price of the steel by 0.5 percent

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