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: United States: PU = 20 - 0.1QU Europe: PE = 10 - 0.05QE where all quantities are expressed in thousands of units (i.e. QU = 10 should be interpreted as 10 thousand hula hoops). The company has a marginal cost of two dollar per unit in the United States (MCU = $2) and four dollars per unit in Europe (MCE= $4). Finally, the firm has a production limitation or constraint of 96 units (96 thousand hula hoops). How many hoops should be sold in the United States?

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amcool amcool · Answer 1 · 2020-09-26T02:52:07+02:00

Answer:

90 units hoops (90 thousand hula hoops) should be sold in the United States.

Explanation:

Demand function given are indirect demand functions. The total revenue can be obtained by multiplying the indirect demand function my the quantity.

Since we wan to calculate the number of hoops that should be sold in the United States, we therefore have:

TRU = QU(20 - 0.1QU)

TRU = 20QU - 0.1QU^2 ......................... (1)

Where TRU denotes the total revenue in the United States.

The marginal revenue in the United States (MRU) can be obtained by differentiating equation (1) with respect to QU as follows:

MRU = dTRU/dQU = 20 - 0.2QU ............ (2)

Note that in the question, the company has a marginal cost of two dollar per unit in the United States given as follows:

MCU = $2

Since profit is maximized at where marginal revenue is equal to the marginal cost, we therefore equate MRU and MCU and solve for QU as follows:

MRU = MCU

This implies;

20 - 0.2QU = 2

-0.2QU = 2 - 20

-0.2QU = -18

QU = -18 / -0.2

QU = 90

This implies that profit is maximized in the US at 90 units hoops (90 thousand hula hoops).

Therefore, 90 units hoops (90 thousand hula hoops) should be sold in the United States.