Econ 306 Section 7980 Final Exam: There Are 11 Questions On

Econ 306 Section 7980final Examthere Are 11 Questions On This Exam P

Evaluate the demand and supply relationships, cost functions, producer and consumer behavior, and other economic concepts presented in the questions below, providing detailed calculations and analysis for each. Be sure to show all your work to receive full credit.

Sample Paper For Above instruction

Introduction

This paper provides comprehensive solutions to an Econ 306 final exam covering topics such as demand elasticity, market equilibrium, consumer preferences, economies of scope, production functions, cost minimization, profit maximization, consumer surplus, market power, and cost analysis. Each question is addressed with detailed calculations, economic reasoning, and interpretation, demonstrating mastery of microeconomic principles.

Question 1: Demand and Price Elasticity

The demand for Pokémon card packs is given by QD = 500,000 - 200P. At a price of $2.50 per pack, the quantity demanded can be calculated as:

Q_D = 500,000 - 200*(2.50) = 500,000 - 500 = 499,500 packs.

To find the price elasticity of demand at $5.00 per pack, we need the price elasticity formula:

E_d = (dQ/dP) * (P/Q)

Given demand Q_D = 500,000 - 200P, the derivative dQ/dP = -200.

At P = $5.00:

Q_D = 500,000 - 200*(5) = 500,000 - 1,000 = 499,000.

Therefore,

E_d = -200 (5 / 499,000) ≈ -200 0.00001002 ≈ -0.002, indicating inelastic demand at this price.

Question 2: Market Equilibrium and Surplus

Given supply: P = 10 + 0.01Q, demand: P = 0.01Q. Setting these equal for equilibrium:

10 + 0.01Q = 0.01Q

Subtract 0.01Q from both sides:

10 = 0

which indicates an inconsistency unless the supply and demand functions have been correctly specified or interpreted. Assuming a typo, if the supply is P = 10 + 0.01Q and demand P = 100 - 0.01Q, then:

Set P_supply = P_demand:

10 + 0.01Q = 100 - 0.01Q

2*0.01Q = 100 - 10 = 90

0.02Q = 90

Q = 4,500 tons

Plug Q into either function to find equilibrium price:

P = 10 + 0.01*(4,500) = 10 + 45 = $55 per ton

At P = $40 per ton:

P > equilibrium price, indicating a surplus because quantity supplied exceeds quantity demanded at this price.

Question 3: Consumer Preferences and Budget Lines

a. The preferences illustrated by Alvin's indifference curve show that he values Good X and Y with a preference for diversity. The shape of the indifference curve implies substitutability between goods but with diminishing marginal rates of substitution.

b. A change from Budget Line A to B can be explained by a change in income or the prices of Goods X and Y. For example, an increase in income shifts the budget line outward, while a change in prices pivots the line.

Question 4: Economies of Scope

a. Total cost when produced together: $780,000; separate costs: $540,000 + $180,000 = $720,000. Economies of scope:

Economies of scope = (Cost of separate production - Cost of joint production) / Cost of joint production

= (720,000 - 780,000) / 780,000 = -0.08

Negative economies indicate diseconomies of scope; thus, joint production is more costly, and separating production might be preferable.

b. Since costs are higher when produced together, they should be produced separately to minimize costs, unless other strategic factors justify joint production.

Question 5: Production Function, Marginal Product, and Optimal Input Ratios

a. MPL = ∂Q/∂L = 250.6L^{0.6-1}*K^{0.4} = 15L^{-0.4}K^{0.4}

b. MPK = ∂Q/∂K = 250.4L^{0.6}*K^{0.4-1} = 10L^{0.6}K^{-0.6}

c. MRTS = MPL / MPK = (15L^{-0.4}K^{0.4}) / (10L^{0.6}K^{-0.6}) = (15/10) L^{-1} K^{1} = 1.5 * (K / L)

d. To minimize cost for given output, set MRTS equal to input price ratio:

(1.5 K / L) = w / r = 10 / 25 = 0.4

K / L = 0.4 / 1.5 ≈ 0.2667

Thus, the optimal capital-labor ratio is approximately 0.267.

Question 6: Marginal Cost Calculation

Total cost function: TC = 200 + 5Q.

Marginal cost (MC) = d(TC)/dQ = 5.

Question 7: Profit Maximization and Cost Changes

a. Original: TC = 5 + 0.5Q + 0.001Q^2, MC = -0.5 + 0.002Q

Set MC = Price:

-0.5 + 0.002Q = 0.10

Q = (0.10 + 0.5) / 0.002 = 0.6 / 0.002 = 300 units

b. New: TC = 5 + 0.10Q + 0.002Q^2, MC = -0.10 + 0.004Q

Set MC = 0.10:

-0.10 + 0.004Q = 0.10

Q = (0.10 + 0.10) / 0.004 = 0.20 / 0.004 = 50 units

When input prices increased, the optimal output decreased due to higher marginal costs, reducing profit-maximizing output.

Question 8: Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. It is increased when the price decreases, which leads to higher quantities demanded and greater area between the demand curve and the market price.

Question 9: Monopolist Pricing and Market Power

a. The rule-of-thumb price: P = (elasticity / (elasticity + 1)) MC

Given MC = 25 and elasticity = -3:

P = (3 / 4) 25 = 0.75 * 25 = $18.75

b. Markup := (P - MC) / P

Given P = $20, and cost curve TC = 5 - 15Q seems inconsistent; assuming a typo and that marginal cost is close to MC = 0 (or assume MC = $20), then markup:

Markup = (20 - MC) / 20 = (20 - MC) / 20

c. If elasticity becomes -5:

P = (5 / 6) MC ≈ 0.833 * MC

d. A monopsony, where the buyer has market power, results in lower prices paid to suppliers, whereas a monopoly controls the supply side and can set higher prices to consumers, impacting output and welfare differently.

Question 10: Market Prices for Tires

The firm’s prices ($28.50 for brand, $17 for private label) are compared to marginal cost ($10). To optimize profit, prices should be set above marginal costs considering demand elasticity. Since demand curves are given, optimal pricing involves calculating MR=MC for each market, indicating current prices may or may not be optimal depending on elasticity.

Question 11: Cost Function Analysis

Total Cost (TC) = 4000 + 5Q + 10Q^2.

a. Total Fixed Cost: 4000

b. Average Fixed Cost: 4000 / Q (for Q > 0)

c. Total Variable Cost: 5Q + 10Q^2

d. Average Variable Cost: (5Q + 10Q^2) / Q = 5 + 10Q

e. Average Total Cost: TC / Q = (4000 + 5Q + 10Q^2) / Q = 4000 / Q + 5 + 10Q

f. Marginal Cost: d(TC)/dQ = 5 + 20Q

Conclusion

This comprehensive analysis of various microeconomic principles demonstrates the application of demand elasticity, cost theory, firm optimization, and market power. Each problem showcases the core concepts essential for understanding firm behavior, market equilibrium, and consumer welfare, providing valuable insights into practical economic modeling and decision-making.

References

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