Questions For Critical Thinking Chapter 4 Discussion Problem

Questions For Critical Thinking Iichapter 4discussionproblems3 A S

Questions for critical thinking II Chapter 4 Discussion Problems 3. (a) Starting with the estimated demand function for Chevrolets given in problem 2, assume that the average value of the independent variables changes to N=225 million, I=$12,000, PF=$10,000, PG=100cents, A=$250,000, and PI=0 (i.e., the incentives are phased out). Find the equation of the new demand curve for Chevrolets. * Revised 3(b): If Pc is $10,000, find the value of Qc. Function from Problem 2 is: Qc= 100, Pc + 2,000N + 50I + 30Pf - 1,000Pg + 3A + 40,000Pi. 7. The total operating revenue of a public transportation authority is $100 million while its total operating costs are $120 million. The price of a ride is $1, and the price elasticity of demand for public transportation has been estimated to be -0.4. By law, the public transportation authority must take steps to eliminate its operating deficit. (a) Should the transportation authority increase or decrease the price per ride based on the price elasticity of demand? (b) Use equation (3-7.) and suggest increasing the price of a ride to $1.50. Your situation will be briefly explained here. 14. Suppose that a firm maximizes its total profits and has a marginal cost (MC) of $8 and the price elasticity of demand (PED) of -3. Find the optimal selling price. Use equation (3-12), where MR equals MC for profit maximization. Chapter 5 Discussion 15. Integrating Problem. Using data for Problem 6 and the prices of a related commodity from 1986 to 2005, a regression was estimated for the demand (X) on the price of the commodity (PX), consumer income (Y), and the price of the related commodity (PZ). The regression results are: X = 121.86 - 9.5PX + 0.04Y - 2.21PZ, with t-values in parentheses: (-5.12) (2.68). R²=0.9633, F=167.33, Durbin-Watson=2.1. (b) Evaluate the regression results in terms of the signs, significance, and explanatory power. The significance is determined by the t-values: coefficients with absolute t-values greater than 2 are significant, such as Px with 5.12, indicating Px significantly affects Qx. If the price of commodity X increases by $1, demand decreases by 9.50 units. (c) Are X and Z substitutes or complements?

Paper For Above instruction

The assignment involves analyzing various economic demand and pricing models based on provided functions and regression results. The primary focus is to analyze how changes in independent variables affect demand, determine optimal pricing strategies considering elasticity, and interpret regression outputs to infer relationships between commodities. This discussion aims to deepen understanding of demand elasticity, profit maximization, and the interdependencies among commodities, which are fundamental concepts in microeconomic theory and applied managerial decision-making.

Starting with the demand function for Chevrolets, given as Qc = 100, Pc + 2,000N + 50I + 30Pf - 1,000Pg + 3A + 40,000Pi, we analyze how changes in the average independent variables alter demand. Assuming the variables N, I, PF, PG, A, and PI change to specified new values, we substitute these into the demand function to derive the new demand curve. Specifically, with N=225 million, I=$12,000, PF=$10,000, PG=100 cents, A=$250,000, and PI=0, the demand becomes a function solely dependent on the price Pc, with the other parameters fixed at their new values. By plugging the new values into the original demand formula, we find the adjusted intercept, leading to a revised demand equation where demand is expressed explicitly as a function of Pc. This approach illustrates how demand responds to shifts in consumer income, population, prices, and incentives.

Regarding the value of Qc when Pc is $10,000, substituting Pc into the revised demand function yields the corresponding quantity demanded, providing critical insights into market responses at different price points. This calculation is essential for pricing strategies and understanding consumer behavior in response to price changes.

In the context of public transportation, the revenue and cost data indicate an operating deficit, prompting considerations about pricing adjustments. Given the price elasticity of demand of -0.4, a relatively inelastic demand suggests that increasing prices could reduce the deficit without large declines in ridership. Using the price elasticity and the current revenue, we determine whether to increase or decrease the fare. Since demand is inelastic, raising the fare—possibly to $1.50—could lead to higher total revenue, thus reducing the deficit, aligning with the rule that inelastic demand favors price increases for revenue enhancement.

Profit maximization models further elucidate optimal pricing strategies. With a marginal cost of $8 and PED of -3, the firm can apply the formula derived from setting marginal revenue equal to marginal cost to determine the profit-maximizing price. The derived formula indicates that the price must be set above marginal cost by a markup that depends on elasticity, which, in this case, results in a price approximately equal to $14. But specific calculations using the elasticity formula confirm the precise value.

In regression analysis of demand for a commodity, the signs and significance of the coefficients provide insights into market dynamics. The regression results, with the estimated coefficients and t-values, suggest a strong, statistically significant relationship between the demand for the commodity and its own price, with a negative sign indicating typical downward-sloping demand. The high R-squared value reflects a model that explains most variability in demand based on the included variables, confirming the adequacy of the model.

Finally, the relationship between two commodities, X and Z, is inferred based on their coefficient signs. A negative coefficient for PZ implies that as the price of the related commodity PZ increases, the demand for X decreases, indicating a complementary relationship. Conversely, a positive coefficient would suggest substitutability. In this case, the negative sign indicates that X and Z are complements: higher PZ reduces demand for X, consistent with typical complementary goods relationships.

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