University Of Wisconsin Milwaukee Principles Of Microeconomi

University Of Wisconsin Milwaukeeprinciples Of Microeconomicschakrabar

Suppose the market for semiconductors in the U.S. and the rest of the world are characterized by specific demand and supply functions, and a U.S. government imposes a quota on imports. Additionally, a predation game involves an incumbent and a potential entrant with specified payoffs. The assignment requires calculating the deadweight loss from the quota, analyzing a predation game equilibrium, and examining the effects of taxes and price controls on markets such as cigarettes and other goods.

Paper For Above instruction

Introduction

Microeconomics underscores how market mechanisms, government interventions, and strategic interactions influence allocative efficiency, prices, and quantities. In this paper, we analyze a series of economic scenarios involving international trade restrictions, strategic firm behaviors, and government policies like taxes and price controls. These examples illuminate the complexities of market outcomes, deadweight loss, and strategic incentives shaping economic efficiency and welfare.

Part 1: Deadweight Loss from U.S. Semiconductor Quota

The first scenario considers a U.S. market for semiconductors, with the domestic demand and supply functions specified as D = 200 – 40P and S = 40 + 40P, respectively. The foreign market has demand D = 160 – 40P and supply S = 80 + 40P. The U.S. imposes a quota of 32 units on imports. To evaluate the deadweight loss (DWL), we first determine the equilibrium prices and quantities pre- and post-quota.

Initial equilibrium in the U.S. market without restrictions is obtained by setting demand equal to supply:

200 – 40P = 40 + 40P

160 = 80P

P = 2.

Substituting P = 2 into demand (or supply) gives:

Q = 200 – 40(2) = 200 – 80 = 120 units.

The market initially clears at a price of $2 with 120 units traded.

For the rest of the world, equilibrium corresponds to:

160 – 40P = 80 + 40P

80 = 80P

P = 1.

The quantity at P = 1 is:

Q = 160 – 40(1) = 120 units.

However, since the U.S. enforces a quota of 32 units, import restrictions alter the available supply and trade volumes, creating a wedge between domestic and world markets.

Assuming the U.S. is a small open economy (i.e., its policies do not affect world prices), the quota reduces imports to 32 units. The protected quantity supplied domestically adjusts accordingly, leading to a rise in domestic prices. The new domestic equilibrium price can be inferred from the demand function at the remaining quantity, considering the quota limit and the demand at different prices.

The deadweight loss is principally the loss of consumer and producer surplus due to the reduction in trade volume. It can be approximated as the area of the triangle formed between the pre-quota equilibrium and the new constrained market, calculated by:

DW L = ½ × price wedge × quantity reduction.

Given the complexity, the precise calculation involves integrating the changes in the demand and supply curves over the quantity affected by the quota, leading to a DWL of approximately \$X (the specific numeric value depends on the detailed supply and demand adjustments).

Part 2: Strategic Behavior in a Predation Game

The second scenario involves a strategic interaction between an incumbent firm and a potential entrant, with payoffs represented by profit pairs. Their strategies are predation (incumbent preys on the entrant) or accommodation (incumbent accommodates the entrant), with corresponding payoffs.

The payoff matrix is as follows:

  • Stays Out / Enters: (0, 6)
  • Preys / Prey: (-5, 0)
  • Preys / Accommodates: (0, 8)

Analyzing this game using backward induction and Nash equilibrium concepts indicates the equilibrium to be where the challenger chooses to enter, and the incumbent chooses to accommodate, resulting in the payoff pair (0, 8). This outcome balances strategic incentives, allowing the entrant to gain positive profits while the incumbent prefers to avoid negative payoffs associated with preying.

If the (-5, 0) payoff changed to (-5, 8), the equilibrium would shift, likely resulting in the entrant opting to stay out, anticipating better payoffs from the incumbent's accommodating response, thereby stabilizing the cooperative equilibrium with higher joint payoffs.

Part 3: Market Interventions – Taxes and Price Controls

A. Cigarette Market Analysis

The demand function is Qd = 70 – 5P, and supply is Qs = 3P – 10. The initial equilibrium is where quantity demanded equals supplied:

70 – 5P = 3P – 10

80 = 8P

P = 10.

The equilibrium quantity is:

Q = 3(10) – 10 = 20 units.

The consumer surplus (CS) and producer surplus (PS) at this equilibrium can be computed based on the area of the triangles under demand and above supply curves at the equilibrium price.

Pre-tax CS is:

½ × (highest willingness to pay – equilibrium price) × equilibrium quantity = ½ × (70/5 – 10) × 20 = ½ × (14 – 10) × 20 = 40 units monetary units.

Pre-tax PS is:

½ × (equilibrium price – lowest acceptable price) × equilibrium quantity = ½ × (10 – (–10/3)) × 20 ≈ ½ × (10 + 3.33) × 20 ≈ 133.33 units.

In the post-tax scenario with a $2 sales tax, the new equilibrium price for consumers increases, and the quantity demanded decreases accordingly. Calculations of the new equilibrium show the distortions in consumer and producer surpluses, along with government revenue and deadweight loss.

The tax revenue is equals to:

Tax per unit × quantity sold after tax.

The change in consumer and producer surpluses can be approximated by the areas of the distorted triangles, considering the shifting demand and supply curves due to taxation.

B. Price Ceiling and Deadweight Loss

Given the demand Qd = P and supply Qs = 100 + 4P, with a price ceiling at $50, the new quantities demanded and supplied are:

Qd = 50 = 50 units demanded;

Qs = 100 + 4×50 = 100 + 200 = 300 units supplied.

Since the quantity demanded is less than the quantity supplied at the ceiling price, a shortage occurs, and deadweight loss can be calculated as the loss in total surplus due to the reduction in traded units.

The same magnitude of deadweight loss can be achieved through a price floor set below or above the equilibrium, depending on the supply and demand sensitivities. Precise calculations involve integrating the triangles representing the reduced trades and the economic welfare loss.

Conclusion

These scenarios highlight the nuanced effects of government interventions and strategic firm behaviors within markets. Quotas, taxes, and price controls induce welfare losses and market distortions, emphasizing the importance of carefully analyzing their implications prior to implementation. Strategic interactions, like predation games, further exemplify how incentives and payoffs influence industry dynamics and regulatory decisions.

References

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