Question

3. You are the manager of one of the major

automobile manufacturing companies in the
country. Your company has developed a new brand
of electric vehicle which you expect will be
competitive in the EV market. However, before
bringing your new product to the market, you
decided to conduct a fresh economic analysis on
the profitability of your new automobile.
Economists in the company provided you with the
following data and estimation relevant for the kind
of economic study you wanted to undertake. You
are told that there is a 20 percent chance of a
recession, a 60 percent chance the economy will
remain as it is, and a 20 percent chance there will
be an economic upturn. If a recession hits, your
inverse demand curve for new car will be P =
100,000 - 4Q. If things remain as they are, your
inverse demand curve will be P 115,000 - 3Q. If
economic growth occurs, your inverse demand
curve will be P = 130,000 2Q. Your cost function
in all three scenarios is C(Q) = 70,000+ 2Q +
0.5Q .
(6 pts)
Assuming that you are risk neutral:
A. How many cars do you expect to produce and
sell?
b. What will be your expected profit maximizing
price?
c. What will be your expected total profit?

Answer 1

To determine the number of cars you expect to produce and sell, calculate the expected quantity demanded at each demand curve multiplied by the probability of each scenario occurring. Find the profit-maximizing price by plugging the quantity into the associated inverse demand curve. Calculate the expected total profit by subtracting the total expected cost from the total expected revenue. After calculation, the answer comes to; no. of cars = 13,333, profit-maximizing price P = $103,334 and Total Profit = $1,377,530,727

Step-by-step explanation:

To determine the number of cars you expect to produce and sell, you need to calculate the expected quantity demanded at each demand curve and multiply it by the probability of each scenario occurring. The expected quantity demanded is calculated by solving each inverse demand curve for quantity (Q). Once you have the expected quantity demanded, you can determine the expected profit-maximizing price by plugging the quantity into the associated inverse demand curve. Finally, to calculate the expected total profit, you subtract the total expected cost from the total expected revenue.

A. To find the expected quantity demanded, solve each inverse demand curve for Q:

If a recession hits: P = 100,000 - 4Q

If things remain as they are: P = 115,000 - 3Q

If economic growth occurs: P = 130,000 2Q

Let's find the Q for each scenario:

Recession: P = 100,000 - 4Q

100,000 - 4Q = 70,000 + 2Q + 0.5Q

6Q = 30,000

Q = 5,000

Remain as they are: P = 115,000 - 3Q

115,000 - 3Q = 70,000 + 2Q + 0.5Q

5.5Q = 45,000

Q = 8,182

Economic growth: P = 130,000 - 2Q

130,000 - 2Q = 70,000 + 2Q + 0.5Q

4.5Q = 60,000

Q = 13,333

B. To find the expected profit-maximizing price, plug the expected quantity into the corresponding inverse demand curve:

Recession: P = 100,000 - 4(5,000)

P = $80,000

Remain as they are: P = 115,000 - 3(8,182)

P = $68,454

Economic growth: P = 130,000 - 2(13,333)

P = $103,334

C. To find the expected total profit, subtract the total expected cost from the total expected revenue:

Let's calculate the total expected cost:

Recession: C(Q) = 70,000 + 2(5,000) + 0.5(5,000)^2

C(Q) = $97,500

Remain as they are: C(Q) = 70,000 + 2(8,182) + 0.5(8,182)^2

C(Q) = $119,386

Economic growth: C(Q) = 70,000 + 2(13,333) + 0.5(13,333)^2

C(Q) = $209,195

Now, let's calculate the total expected revenue:

Recession: Revenue = P * Q = $80,000 * 5,000

Revenue = $400,000,000

Remain as they are: Revenue = P * Q = $68,454 * 8,182

Revenue = $559,046,728

Economic growth: Revenue = P * Q = $103,334 * 13,333

Revenue = $1,377,739,922

Finally, let's subtract the total expected cost from the total expected revenue:

Recession: Total Profit = $400,000,000 - $97,500 = $399,902,500

Remain as they are: Total Profit = $559,046,728 - $119,386 = $558,927,342

Economic growth: Total Profit = $1,377,739,922 - $209,195 = $1,377,530,727