Question

II. Solve the following problems

a. The supply and demand equations for a certain product are:

3q - 200p + 1800= 0

3q + 100p - 1800= 0

Respectively, where p represents the price per unit in dollars and q the number of units sold per period. Find the equilibrium price.

b. A manufacturer of children’s toys will break even at a sales volume of $200,000. Fixed costs are $40,000 and each unit of production sells for $5. Determine the variable cost per unit.

Answer 1

II)

a)

3q-200p+1800=0 ----(1)

3q+100p-1800=0   ----(2)

Subtract equation (2) from equation (1)

(3q-200p+1800)-(3q+100p-1800)=0

-300p+3600=0

p*=12

Now set p=12 in equation (2)

3q+100*12-1800=0

3q-600=0

q*=200

So,

Equilibrium price=p*=$12

Equilibrium quantity=q*=200

b)

Break even sales=BES=$200000

Price P=$5

Break even sales in units=BES/p=200000/5=40000

Let variable cost per unit be V. We know that

BEP=Fixed cost/(P-V)

40000=40000/(5-V)

5-V=1

V=$4 (Variable cost per unit)