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.

1. What are the profit-maximizing prices and quantities in the two markets?
2. 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_U²

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_E²

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.