Question #71168

the Osram lamp company, estimated the following demand function for its product:
Q=120000-10000p
where Q is the quantity demanded per year and P is the price per lamp. the firm's fixed cost is $12000 and variable cost is $1.50 per lamp.
a) write an equation for the total revenue (TR) function in term of Q.
b) state the marginal revenue function
c)write an equation for the total cost (TC) function in term of Q.
d)state the marginal cost function.
e) write an equation for total profits (π) in term of Q. at what level of outputs (unitd) and price ($) are total profits maximised? calculate the total profits at this output level

Expert's answer

Qd = 120000 -10000P, P = 12 - 0.0001Q, FC = $12000, AVC = $1.50 per lamp.

a) TR function in term of Q is:

TR = P*Q = 12Q - 0.0001Q^2.

b) MR = TR' = 12 - 0.0002Q.

c) TC = FC + VC = FC + AVC*Q = 12000 + 1.5Q.

d) MC = TC' = 1.5.

e) total profits π = TR - TC = 12Q - 0.0001Q^2 - 12000 - 1.5Q = 10.5Q - 0.0001Q^2 - 12000.

Total profits are maximised when MR = MC, so: 12 - 0.0002Q = 1.5,

0.0002Q = 10.5,

Q = 52500 units.

π = 10.5*52500 - 0.0001*52500^2 - 12000 = $263625.

a) TR function in term of Q is:

TR = P*Q = 12Q - 0.0001Q^2.

b) MR = TR' = 12 - 0.0002Q.

c) TC = FC + VC = FC + AVC*Q = 12000 + 1.5Q.

d) MC = TC' = 1.5.

e) total profits π = TR - TC = 12Q - 0.0001Q^2 - 12000 - 1.5Q = 10.5Q - 0.0001Q^2 - 12000.

Total profits are maximised when MR = MC, so: 12 - 0.0002Q = 1.5,

0.0002Q = 10.5,

Q = 52500 units.

π = 10.5*52500 - 0.0001*52500^2 - 12000 = $263625.

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