Question

5. Hula Products has reintroduced the hula hoop to the world and faces a growing demand for its product in two distinct markets: the United States and Europe. Demand in these markets is:

P_{U} = 20 - .1Q_{U}

and
P_{E} = 10 - .05Q_{E}.,

where all quantities are expressed in thousands of units (i.e.
Q_{U} = 50 means 50 thousand units). Hula can produce hoops
at a marginal cost of $1.50 per unit.

- What are the profit-maximizing prices and quantities in the two markets?
- Hula has a capacity constraint and can produce a maximum of 200 thousand hoops. How does this affect the firm’s output and prices in part a?

Explain why

Answer #1

5. In US, P_{U}=20-0.1Q_{U}

Now, Total revenue TR_{U} = P_{U}*Q_{U}
= 20Q_{U}-0.1Q_{U}^{2}

and Marginal revenue MR_{U} =
dTR_{U}/dQ_{U} = 20-0.2Q_{U}

Then, for equilibrium,

MR_{U} = MC

or, 20-0.2Q_{U} = 1.5

or, 0.2Q_{U} = 18.5

or, Q_{U} = 92.5 thousand units

and P_{U}=20-(0.1*92.5) = 20-9.25 = $10.75 per unit

In Europe, P_{E}=10-0.05Q_{E}

Now, TR_{E} = P_{E}*Q_{E} =
10Q_{E}-0.05Q_{E}^{2}

and MR_{E} = 10-0.1Q_{E}

Then, for equilibrium,

MR_{E} = MC

or, 10-0.1Q_{E} = 1.5

or, 0.1Q_{E} = 8.5

or, Q_{E} = 85 thousand units

and P_{E} = 10-(0.05*85) = $5.75 per unit

Capacity constraint of the firm does not affect the equilibrium price and quantity. This is because the total equilibrium in both units is less than 200.

Hula Products has reintroduced the hula hoop to the world and
faces a growing demand for its product in two distinct markets: the
United States and Europe. Demand in these markets is:
PU = 20 - .1QU
PE = 10 - .05QE
where all quantities are expressed in thousands of units (i.e.
QU = 50 means 50 thousand units).
The company has an existing stock of 95 thousand hula hoops. How
many should be sent to Europe?

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quantities are expressed in thousands of units (i.e. QUQU = 50
means 50 thousand units). The company has an existing stock of 95
thousand hula hoops. How many should be sent to Europe?
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