Supply and Demand Essay

3081 Words Jan 23rd, 2014 13 Pages
1. A firm's current profits are \$1,000,000. These profits are expected to grow indefinitely at a constant annual rate of 3.5 percent. If the firm's opportunity cost of funds is 5.5 percent, determine the value of the firm:

Instructions: Round your responses to 2 decimal places.

a. The instant before it pays out current profits as dividends. \$ million

b. The instant after it pays out current profits as dividends.

\$ million
(page 18)
Explanation:
a. The value of the firm before it pays out current dividends is:

PVfirm = \$1,000,000((1 + 0.06) / (0.06 - 0.04) = \$52.75 million

b. The value of the firm immediately after paying the dividend
(This one is tricky.)

Instructions: Round your responses to 2 decimal places.

b. Profits grow at an annual rate of 2 percent.

billion

c. Profits grow at an annual rate of 0 percent.

billion

d. Profits decline at an annual rate of 5 percent.

billion Explanation:
a. Since the profits grow faster than the interest rate, the value of the firm would be infinite. This illustrates a limitation of using these simple formulas to estimate the value of a firm when the assumed growth rate is greater than the interest rate.

b. PVfirm = π((1 + i) / (i - g)) = \$4.5(1.08 / 0.06) = \$81 billion

c. PVfirm = π((1 + i) / (i - g)) = \$4.5(1.08 / 0.08) = \$60.75 billion

d. PVfirm = π((1 + i) / (i - g)) = \$4.5(1.08 / 0.13) = \$37.38 billion

7. The demand curve for product X is given by QXd = 420 - 4PX.

a. Find the inverse demand curve.

PX = - QXd

b. How much consumer surplus do consumers receive when Px = \$50?

\$

c. How much consumer surplus do consumers receive when Px = \$25?

\$

d. In general, what happens to the level of consumer surplus as the price of a good falls?

The level of consumer surplus as the price of a good falls.
Explanation:
a. Solve the demand function for Px to obtain the following inverse demand function: PX = 105 - 0.25QXd.

b. Notice that when Px = \$50, QXd = 420 - 4(50) = 220 units. Also, from part a, we know

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