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1. We focus on the market of a particular good in Country A. Back in 2019 , the...
Aug 14, 2024
1 Solution
a
Competitive Equilibrium: To find the competitive equilibrium, we set the demand equal to the supply: 10−3p=2p10 - 3p = 2p. Solving for pp, we get 10=5p10 = 5p or p=2p = 2. Substituting pp back into either equation gives Q=10−3(2)=4Q = 10 - 3(2) = 4. Thus, the equilibrium price is p=2p = 2 and quantity is Q=4Q = 4
b
Reasonable Supply Curves: After the trade war, the supply curve shifts leftward. The new supply curves must be above the original supply curve S=2pS = 2p at p=2p = 2. The reasonable estimates from the graphs are those that start from the origin and are above the red line at p=2p = 2. The green dashed lines in Ann's, Bob's, and David's graphs are reasonable, while Chris's is not, as it does not meet this criterion
c
New Equilibrium Comparison: For the reasonable supply curves (Ann, Bob, and David), the new equilibrium price will be higher than the old equilibrium price of p=2p = 2 due to the decrease in supply. The quantity will be lower than the original equilibrium quantity of Q=4Q = 4
Answer
Equilibrium Price: p=2p = 2, Quantity: Q=4Q = 4; New equilibrium price > 2, Quantity < 4
Key Concept
Competitive equilibrium occurs where demand equals supply, determining market price and quantity.
Explanation
The equilibrium price and quantity change due to shifts in supply, affecting market dynamics post-trade war.
2 Solution
a
Consumer Surplus Calculation: The consumer surplus is the area above the price and below the demand curve. At p=5p = 5, Q=20−2(5)=10Q = 20 - 2(5) = 10. At p=7p = 7, Q=20−2(7)=6Q = 20 - 2(7) = 6. The consumer surplus at p=5p = 5 is 12×10×(10−5)=25\frac{1}{2} \times 10 \times (10 - 5) = 25 and at p=7p = 7 is 12×6×(10−7)=9\frac{1}{2} \times 6 \times (10 - 7) = 9. The change in consumer surplus is 9−25=−169 - 25 = -16
Answer
Change in Consumer Surplus: −16-16
Key Concept
Consumer surplus measures the benefit to consumers from purchasing at a lower price than they are willing to pay.
Explanation
An increase in price reduces consumer surplus, indicating a loss of welfare for consumers.
3 Solution
a
Production Decision in Perfect Competition: In perfect competition, produce where p=MCp = MC. Set MC(q)=pMC(q) = p. The marginal cost function is MC(q)=q2−4q+5MC(q) = q^2 - 4q + 5. For p≥5p \geq 5, solve q2−4q+5=pq^2 - 4q + 5 = p. If p < 5, shut down as MCMC exceeds price
b
Profit Check at p=9.8p = 9.8: At p=9.8p = 9.8, check if MC(5)=52−4(5)+5=5MC(5) = 5^2 - 4(5) + 5 = 5. Since MC=5MC = 5 and p=9.8p = 9.8, you can make a profit. If selling q=5q = 5 at p=9.8p = 9.8, profit is (9.8−5)×5=24(9.8 - 5) \times 5 = 24
c
Evaluate David's Recommendation: If lowering the price to p=9.8p = 9.8 increases quantity to q=7q = 7, check profit: (9.8−MC(7))×7(9.8 - MC(7)) \times 7. Calculate MC(7)=72−4(7)+5=5MC(7) = 7^2 - 4(7) + 5 = 5. Profit becomes (9.8−5)×7=33.6(9.8 - 5) \times 7 = 33.6, which is higher than at p=10p = 10. Thus, David's recommendation is beneficial
Answer
Profit at p=9.8p = 9.8 is higher than at p=10p = 10; David's recommendation is beneficial.
Key Concept
In imperfect competition, pricing strategies can significantly affect profit margins and production decisions.
Explanation
Adjusting prices can lead to increased sales and profits, demonstrating the importance of market conditions in decision-making.
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