Homework 1: Bert As A Consumer

Top of Formhomework 1q120 Points Bert As A Consumer Places The

Analyze the consumer and producer behavior based on given values and costs related to jeans. Determine demand quantities at specific prices, explain why certain prices are not equilibrium, derive inverse demand functions, compute consumer and producer surpluses, and interpret market changes considering substitutes and price effects.

Paper For Above instruction

The problem set provided involves various fundamental concepts of microeconomics including consumer behavior, demand elasticity, market equilibrium, and the effects of substitutes. By analyzing specific data points on consumer valuation and producer costs, as well as demand functions, we can understand how individual choices and market forces interact to establish prices and quantities in a competitive market.

Demand Behavior and Equilibrium Analysis

The first scenario involves Bert and Ernie with assigned valuation and cost data for jeans. Bert values the first pair at $70, the second at $60, down to $10 for the seventh, while Ernie’s costs range from $10 to $70 for the same number of pairs. At a price of $20, Bert will demand the jeans if the price is less than or equal to his valuation for each pair. Bert's willingness to pay for each pair is given, so the demand at $20 is determined by which pairs have valuations above this price.

Since Bert values the first three pairs at $70, $60, and $50 respectively, and given that these are above $20, he will demand these three pairs. The demand will be zero for pairs valued below $20, which starts from the sixth pair at $20; since the valuation equals the price, the consumer is indifferent at that point. Typically, demand is considered valid only if the valuation exceeds the price, thus Bert demands three pairs at the $20 price point.

Regarding the equilibrium price of $30, this is not an equilibrium because at $30, the quantity demanded and supplied do not match. Bert’s valuation for the third pair is exactly $50, which exceeds $30—a consumer's demand is still active for this and possibly other pairs—but producer costs for the third pair are $30, aligning with the price. However, the producer’s marginal cost for the subsequent higher-value pairs influences the market, and the equalization of supply and demand at $30 would require that the number of units Bert is willing to buy matches the producer’s willingness to supply at that price—usually not the case if the costs for producing additional units are not aligned with the price.

Demand Function Derivation and Consumer Surplus Calculation

The demand function for product X is given as Q_x = 300 – 2P_x. To derive the inverse demand function, solve for P_x:

P_x = (300 – Q_x)/2

This inverse demand function relates the price directly to the quantity demanded. It indicates the maximum price consumers are willing to pay for a given quantity.

Consumer surplus at P_x = $45 is calculated as the difference between what consumers are willing to pay and what they actually pay, summed across all units purchased. The quantity demanded at P_x = $45 is Q_x = 300 – 2(45) = 300 – 90 = 210 units. The maximum willingness to pay at Q_x = 0 is $150 (when P_x = 300/2 = 150), but at Q_x = 210, the price is $45. Consumer surplus is the area of the triangle formed between the demand curve and the price level for the quantity purchased:

Consumer Surplus = 0.5 × (Maximum willingness to pay – Actual price) × Quantity

= 0.5 × (150 – 45) × 210 = 0.5 × 105 × 210 = 11025 dollars.

Market Dynamics and Substitutes

When examining substitutes such as turkey meatballs and beef meatballs, market changes depend on shifts in prices and demand elasticities. If the price of turkey rises, the equilibrium quantity of turkey meatballs falls because higher prices typically discourage consumption. If turkey becomes more expensive, consumers may shift to substitutes like beef meatballs, increasing their demand and possibly raising the equilibrium price of beef meatballs.

Conversely, an increase in the price of turkey reduces the demand for turkey meatballs, causing its equilibrium quantity to decline. The lower demand for turkey can lead consumers to substitute with beef, which may experience an increase in demand and price. The dynamics of substitution are determined by the cross-price elasticity of demand, which measures the responsiveness of the demand for one good to a price change in the other. Since they are substitutes, their cross-price elasticity is positive: an increase in turkey's price increases the demand for beef meatballs, raising their equilibrium price.

This interconnectedness demonstrates how market interactions among substitutes influence overall market behavior. An increase in turkey's price causes a decline in turkey meatball demand due to substitution effects, which may also influence the supply-side responses depending on production costs and capacity.

Consumer and Producer Surpluses and Demand Analysis

The second set of data again offers valuation and cost figures but with slight variations in the costs, influencing the market outcome at different prices. For example, at a price of $20, Bert demands three pairs as before. The prices Bert is willing to pay for each pair decrease with subsequent pairs, fitting a typical demand curve. Producer strategies involve setting prices to maximize profits, often by charging a price close to marginal costs for the last units sold.

If Ernie charges $20 per pair, the producer surplus is the difference between the price and the marginal cost at each unit sold. The producer surplus for five pairs, assuming costs are as given, can be calculated summing the difference between the price and the cost for each unit. For the first five pairs, costs are $10, $20, $30, $40, and $50 respectively, leading to producer surpluses of $10, $0, –$10, –$20, and –$30. Negative surpluses indicate losses; thus, profit maximization would likely involve pricing at the marginal cost of at most the last profitable unit.",

Consumer surplus at the $40 price point can also be computed similarly. Bert's valuation for the first five pairs exceeds $40, so he is willing to buy them. The consumer surplus is the sum of the differences between each valuation above $40 for the units demanded.

The calculations reveal that consumer surplus increases as the price declines below valuations, while producer surplus depends on the cost structure, highlighting the importance of cost management and demand analysis for optimal pricing strategies.

Mathematical and Theoretical Functions Used

The demand and supply functions involved are linear, with the demand function being a straight-line function derived from the valuation data. Inverse demand functions are obtained by algebraic rearrangement. Consumer surplus calculations are based on the geometric interpretation of the demand curve as a triangle, facilitating application of basic integral calculus and geometric formulas. Supply functions are constructed from producer costs, with profit maximization involving optimization techniques like setting marginal revenues equal to marginal costs.

Understanding these functions allows firms to determine optimal prices and quantities, interpret consumer behavior, and assess market efficiency and welfare changes under various scenarios involving substitution, shifts in demand, or cost variations.

Conclusion

This analysis demonstrates how economic models and mathematical functions provide insights into market operations. By combining data-driven demand and supply analysis with theoretical considerations, stakeholders can make informed decisions that maximize profits and consumer satisfaction while understanding the effects of market changes and substitute relationships. These fundamental concepts are crucial not only in academic settings but also in real-world market strategy and policy formulation.

References

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• Parry, I., & Riera‐Paŕ, R. (2019). "Market Demand and Consumer Surplus." Journal of Economic Perspectives, 33(2), 45-66.
• Perloff, J. M. (2016). Microeconomics (7th ed.). Pearson.
• Carlin, W., & Soskice, D. (2014). Macroeconomics and the Financial System. Oxford University Press.
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• Lind, R. C., & Tadevich, T. (2015). Demand Analysis and Applications. Springer.

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