Question

The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following demand function for its product:

Q = 120,000 – 10,000P

where Q is the quantity demanded per year and P is the price per lamp.

The firm’s fixed costs are $12,000 and variable costs are $1.50 per lamp.

a. Write an equation for the total revenue (TR) function in terms of Q.
b. Specify the marginal revenue function.
c. Write an equation for the total cost (TC) function in terms of Q.
d. Specify the marginal cost function.
e. Write an equation for total profits (π) in terms of Q. At what level of output (Q) are total profits maximized? What price will be charged? What are total profits at this output level?
f. Check your answers in Part (e) by equating the marginal revenue and marginal cost functions, determined in Parts (b) and (d), and solving for Q.
g. What model of market pricing behavior has been assumed in this problem?

Answer 1

Answer on Question #63242, Economics / Microeconomics

The Lumins Lamp Company, a producer of old-style oil lamps, estimated the following demand function for its product: $Q = 120,000 - 10,000P$

where $Q$ is the quantity demanded per year and $P$ is the price per lamp.

The firm's fixed costs are $12,000 and variable costs are $1.50 per lamp.

a. Write an equation for the total revenue (TR) function in terms of Q.

b. Specify the marginal revenue function.

c. Write an equation for the total cost (TC) function in terms of Q.

d. Specify the marginal cost function.

e. Write an equation for total profits ($\pi$) in terms of Q. At what level of output (Q) are total profits maximized? What price will be charged? What are total profits at this output level?

f. Check your answers in Part (e) by equating the marginal revenue and marginal cost functions, determined in Parts (b) and (d), and solving for Q.

g. What model of market pricing behavior has been assumed in this problem?

Answer:

a. $TR = P \times Q = (12 - Q/10,000) \times Q = 12Q - Q^2/10,000$

b. $MR = TR' = 12 - Q/5,000$

c. $TC = FC + VC = 12,000 + 1.5Q$

d. $MC = TC' = 1.5$

e. $\pi = TR - TC = 12Q - Q^2/10,000 - 12,000 - 1.5Q = -Q^2/10,000 + 10.5Q - 12,000$

Total profits are maximized, when

$$MR = MC,$$ $$12 - Q/5,000 = 1.5$$ $$Q/5,000 = 10.5$$ $$Q = 10.5 \times 5,000 = 52,500 \text{ units}$$ $$P = 12 - Qd/10,000 = 12 - 52,500/10,000 = \$6.75$$ $$\pi = -52,500^2/10,000 + 10.5 \times 52,500 - 12,000 = \$263,625$$

f. $MR = 12 - 52,500/5,000 = 1.5$, $MC = 1.5$

g. $P = \$6.25$ and is higher than $MR = MC = 1.5$

This is monopolistic market.

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