Question 1a: Firm Has Three Investment Alternatives As Indic

Question 1a Firm Has Three Investment Alternatives As Indicated In T

Question 1: A firm has three investment alternatives, as indicated in the following payoff table (payoffs in thousands of dollars): To understand this table, let's look at the first investment possibility, a (designated decision 1, or d1). First of all, there are three possible scenarios: s1, economic conditions improve; s2, conditions remain stable; s3, the economy nosedives. The respective probabilities for each scenario are 0.4, 0.3, and 0.3. Under d1, if the economy improves, the payoff will be 100K; if stable, 25K, if the economy is poor, the payoff is 0. The second investment strategy is somewhat less sensitive to economic conditions, and the third is not influenced by the economy at all, guaranteeing a 50K payoff. Using the expected value approach, which decision is preferred?

Paper For Above instruction

The decision-making process in investment strategies involves evaluating potential outcomes based on their expected values. The problem presents three investment alternatives with different payoffs depending on economic scenarios and associated probabilities. To determine the preferred investment choice using the expected value (EV) approach, we need to compute the EV for each alternative by considering the payoffs and their probabilities.

Investment Alternative 1 (d1): Under this option, the payoffs are ¥100K if the economy improves (s1), ¥25K if stable (s2), and ¥0 if the economy declines (s3). The probabilities for these scenarios are 0.4, 0.3, and 0.3 respectively. The expected value is calculated as:

EV_d1 = (0.4 × 100) + (0.3 × 25) + (0.3 × 0) = 40 + 7.5 + 0 = ¥47.5K

Investment Alternative 2: This alternative is less sensitive to economic changes. Suppose it yields ¥50K in the best case and ¥25K in the stable case, with the worst case similar to the current alternative (¥0). If its payoffs are ¥50K for s1, ¥25K for s2, and ¥0 for s3, then its EV is:

EV_d2 = (0.4 × 50) + (0.3 × 25) + (0.3 × 0) = 20 + 7.5 + 0 = ¥27.5K

Investment Alternative 3: This option offers a fixed payoff regardless of economic conditions, amounting to ¥50K in all scenarios. Its EV simplifies to:

EV_d3 = (0.4 × 50) + (0.3 × 50) + (0.3 × 50) = 50

Thus, using the expected value criterion, the third alternative (d3) with a consistent payoff of ¥50K yields the highest EV of ¥50K, making it the preferred choice based on expected monetary value.

Question 2: Revisiting the payoff table from LST 4-1 (payoffs in thousands of dollars), decision makers face choices involving a lottery with payoffs of ¥100K with probability p and ¥0 with probability (1-p). Two decision makers have expressed their indifference probabilities, and we are asked to find the most preferred decision for each using the expected utility approach. To do this, we substitute each decision maker’s indifference probability multiplied by ten for the corresponding actual values in the payoff table. Then, we compute the expected utility for each alternative using these new values and the actual probabilities.

Part A: Expected Utility Calculation for Each Decision Maker

Assume Decision Maker A’s indifference probability p_A is, for example, 0.6, and Decision Maker B’s p_B is 0.3. Multiplying these by ten gives scaled values: 6 for A and 3 for B. These values are used as the modified payoffs in the utility calculations.

For Decision Maker A, the expected utility (EU) of the lottery can be computed as:

EU_A = (p_A × U(¥100K)) + (1 - p_A) × U(¥0)

Using the scaled values: U(¥100K) = 6, U(¥0) = 0, thus:

EU_A

= (0.6 × 6) + (0.4 × 0) = 3.6 + 0 = 3.6

Similarly, for Decision Maker B:

EU_B

= (0.3 × 3) + (0.7 × 0) = 0.9 + 0 = 0.9

Comparing these expected utilities, the decision with the higher EU is preferred—here, Decision Maker A with an EU of 3.6 is more risk-tolerant than B with an EU of 0.9.

Part B: Risk Attitudes and Decision Preference

The difference in decision choices between A and B reflects their attitudes toward risk. Decision Maker A, possessing a higher indifference probability and consequently a higher expected utility, displays risk-seeking behavior, being more willing to accept uncertain prospects with higher potential payoffs. Conversely, B's lower indifference probability indicates a risk-averse attitude, favoring safer, certain outcomes over uncertain ones. These attitudes influence their decision preferences, with risk-takers valuing higher potential gains despite uncertainty, while risk-averse decision makers prioritize certainty, even at the expense of lower expected payoffs.

Part 3: Market Equilibrium with Price Floor and Deadweight Loss

In the specified market, supply and demand are characterized by the equations:

• Q_S = -14 + P_X
• Q_D = 82 - 2P_X

A price floor of $37 is imposed, and the government purchases any unsold units at this price. To analyze the impact:

a. Cost to the government of buying unsold units

First, find the quantities demanded and supplied at the price floor of $37:

Q_S = -14 + 37 = 23 units

Q_D = 82 - 2 × 37 = 82 - 74 = 8 units

Since the supply exceeds demand at this price, the government must purchase the excess:

Unsold units = Q_S - Q_D = 23 - 8 = 15 units

Thus, the cost to the government = 15 × $37 = $555

b. Deadweight loss from the price floor

Deadweight loss (DWL) results from the reduction in mutually beneficial transactions caused by the price floor. The equilibrium without intervention occurs where supply equals demand:

-14 + P_X = 82 - 2P_X

Solving for P_X: P_X + 2P_X = 82 + 14 = 96

3P_X = 96 ⇒ P_X = 32

At equilibrium price of $32, quantity demanded and supplied are:

Q_S = -14 + 32 = 18 units

Q_D = 82 - 2 × 32 = 82 - 64 = 18 units

This confirms equilibrium quantity is 18 units. When the price is artificially raised to $37, the quantity demanded drops to 8 units, and supplied increases to 23 units, creating a surplus of 15 units, as previously calculated. The DWL is the loss in consumer and producer surplus due to the reduction in traded units from 18 to 8. The DWL area can be represented as the triangle with base (18 - 8) = 10 units and height of the difference between the price and the marginal valuation margin, approximated as:

DWL = (1/2) × (quantity reduction) × (price difference) = (1/2) × 10 × (37 - 32) = 5 × 5 = $25

This deadweight loss quantifies the economic inefficiency caused by the price floor.

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