Assume that the price per unit, D, of a certain item to the consumer is given by

Question

Assume that the price per unit, D, of a certain item to the consumer is given by the equation: , where x is the number of units in demand. The price per unit, S, from the supplier is given by the equation: , where x is the number of units supplied. Find the equilibrium price and the equilibrium quantity

Explanation / Answer

SOLUTIONS 1) f(x)=x^3+3x^2-1 with -3= (d) 3x(x+2)=0=> (e) x=0 or x=-2 f"(0)=6>0 & f(0)=-1=> f(0)=-1 is a minimum. f"(-2)=-6 f(-2)=3 is a maximum 2) Let r=xp=48x/(0.01x^2+1) with 0= x=10 (reject the -ve root) 10 thousands of watch must be sold. 3) Let c=C(x)/x , then c=0.2(0.01x^2+117)/x=> c'=0.002-23.4/x^2=> c"=46.8/x^3 c'=0=> x^2=23.4/0.002=> x=108.166...=> x=108 unit The products produced are 108 units.

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