Question

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 + 0.5Q2. .

(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 to produce and sell, calculate the expected demand under each economic scenario.

Calculate the expected profit-maximizing price by finding the price that corresponds to the quantity demanded at each scenario. Calculate the expected total profit by subtracting the total cost from the total revenue for each scenario and multiplying by the probability of that scenario.

Determining the optimal number of cars to produce and the corresponding profit-maximizing price involves analyzing demand equations across different economic scenarios.

For a recession, represented by the demand equation P = 100,000 - 4Q, and assuming probabilities for each scenario, the quantity demanded can be calculated.

Similarly, for the current economy, with the equation P = 115,000 - 3Q, and an economic upturn, denoted by P = 130,000 - 2Q, quantities demanded can be determined based on respective probabilities.

To ascertain the profit-maximizing price in each scenario, we find the price that aligns with the quantity demanded, considering the demand equations. This step yields the price that optimizes revenue under varying economic conditions.

Subsequently, the expected total profit is computed by subtracting total costs (C(Q)) from the total revenue generated (price * quantity) for each scenario. These results are then multiplied by the respective probabilities of each economic scenario.

By factoring in probabilities, demand equations, and associated costs, this approach allows for a comprehensive evaluation of expected total profits across diverse economic conditions.

It aids decision-making in determining optimal production quantities and pricing strategies to maximize profitability, considering the uncertainties of varying economic scenarios.