Question

Unique Creations holds a monopoly position in the production and sale of magnometers.
The cost function facing Unique is estimated to be
TC = $100,000 + 20Q
a. What is the marginal cost for Unique?
b. If the price elasticity of demand for Unique is currently –1.5, what price
should Unique charge?
c. What is the marginal revenue at the price computed in Part (b)?
d. If a competitor develops a substitute for the magnometer and the price
elasticity increases to –3.0, what price should Unique charge?

Answer 1

Answer on question #76005- Economics – Microeconomics.

Unique Creations holds a monopoly position in the production and sale of magnometers.

The cost function facing Unique is estimated to be

$$\mathrm {T C} = \mathrm {S} 1 0 0, 0 0 0 + 2 0 \mathrm {Q}$$

A) Question: What is the marginal cost for Unique?

Solution: Marginal Cost for Unique

$$\mathrm {T C} = \$ 1 0 0, 0 0 0 + 2 0 \mathrm {Q}$$

Differentiate the total cost function

$$\begin{array}{l} \mathrm {M C} = \mathrm {d} / \mathrm {d Q} (\$ 1 0 0, 0 0 0 + 2 0 \mathrm {Q}) \\ = 2 0 \\ \end{array}$$

Answer: Marginal Cost 20

B) Question: If the price elasticity of demand for Unique is currently $-1.5$, what price should Unique charge?

Solution: Price to be charged

$$\mathrm {M R} = \mathrm {p} (1 + 1 / \mathrm {E d}) \text{ this is equation 1}$$

The marginal revenue (MR) is expressed as the $20 while the elasticity of demand (Ed) which is -1.5.

Then we substitute the values of MR and demand elasticity in equation 1

$$\mathrm{MR} = \mathrm{p}(1 + 1/\mathrm{Ed})$$ $$20 = \mathrm{p}(1 + 1/-1.5)$$ $$20 = \mathrm{p}(0.5/1.5)$$ $$20 * 1.5 = \mathrm{P.5}$$ $$30 = \mathrm{p.5}$$ $$\mathrm{P} = 30/0.5$$

Answer: Unique must charge price $60

C) Question: What is the marginal revenue at the price computed in Part (b)?

Solution: Marginal Revenue at price $60

$$\mathrm{MR} = \mathrm{P}(1 + 1/\mathrm{Ed})$$ $$60(1 + 1/-1.5)$$ $$60 * (0.5//1.5)$$

Answer: At price of $60, Marginal revenue is $20

D) Question: If a competitor develops a substitute for the magnometer and the price elasticity increases to $-3.0$, what price should Unique charge?

Solution: Change in demand elasticity due to substitutes

Marginal revenue must be equal to marginal cost to achieve equilibrium

$$\mathrm{MR} = \mathrm{P}(1 + 1/\mathrm{Ed})$$ $$20 = \mathrm{MC}$$ $$\mathrm{P}(1 + 1/-3) = 20$$ $$\mathrm{p}(2/3)$$ $$20$$ $$\mathrm{P} = 60/30$$ $$= 30$$

Answer: The price Unique should charge has gone down to $30

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