Problem Set 1 Due January 19, 2017 - ECN 312 Intermediate Mi

Problem Set 1 Due January 19 2017ecn 312 Intermediate Microeconom

Consider the market for apartments in Tempe. There is only one local apartment owner, Lord Land, who supplies apartments on a monthly basis. The number of apartments supplied depends on the monthly rental price for apartments (R). Tenants rent apartments by the month. The number of apartments demanded in a given month depends on the monthly rental price of apartments (R) and on the number of tenants looking for apartments (T).

The equations describing the supply and demand relationships are as follows: Qs = 5R + 300 and Qd = 3T - 15R.

Please address the following questions:

- (a) What is the demand for apartments when there are 3,100 tenants looking for apartments that month? Your answer should be a function of R.

- (b) What is the equilibrium rent when T=3,100? What is the equilibrium quantity of apartments when T=3,100? Show these solutions graphically.

- (c) With a rent-control policy of no more than $400 per month, how many apartments are rented when T=3,100? Show this graphically.

- (d) With a minimum-rent policy requiring tenants to pay at least $620 per month, how many apartments are rented when T=3,100? Would this policy be successful? Describe briefly.

- (e) What is the effect of the policy in (d) when there are 6,200 tenants? Describe briefly.

Additionally:

The labor market for food truck workers at a 3-day music festival in Tempe Beach Park involves supply and demand equations:

Q_s = 15P + 10W and Q_d = 1F - 5P^2.

- (a) What is the supply of labor hours when W=15? What is the demand when F=900? Provide answers as functions of P.

- (b) Find the equilibrium price and quantity of labor hours when W=15 and F=900. How many hours does each worker supply? Show graphically.

- (c) When W=11 and F=900, what are the new equilibrium wage and employment?

- (d) Increasing expected attendees from 900 to 1,500, what are the effects on equilibrium wages and hours? Show graphically.

- (e) Increasing attendees to 4,700, how many hours would each worker supply? Explain briefly if this makes sense.

Paper For Above instruction

This paper addresses two interconnected microeconomic markets: the apartment rental market in Tempe and the labor market for food truck workers at a local festival. Each scenario involves supply and demand functions, equilibrium determination, and policy implications, analyzed with a focus on how shifts in parameters affect market outcomes.

Market for Apartments in Tempe

The apartment market in Tempe is modeled with demand and supply functions that depend on prices and quantities. The supply function, Qs = 5R + 300, indicates that landlords supply more apartments as rental prices increase. The demand function, Qd = 3T - 15R, shows that demand depends on the number of tenants (T) and rental prices, which inversely affect demand.

Part (a): Demand Function at T=3,100

Given T=3,100 tenants, the demand for apartments becomes Qd = 3(3100) - 15R, which simplifies to Qd = 9300 - 15R. This function indicates that demand decreases as rental price R increases, with the number of tenants determining the overall demand level.

Part (b): Equilibrium Rent and Quantity

At equilibrium, Qs = Qd, so:

5R + 300 = 9300 - 15R

Solving for R:

20R = 9000

R = 450

Substituting R back into either equation gives equilibrium quantity:

Q = 5(450) + 300 = 2250 + 300 = 2550 apartments.

Graphically, the supply line slopes upward, intersecting the demand line at R=450, with 2550 apartments exchanged.

Part (c): Rent-Control at $400

With a maximum rent R=400:

Qd = 9300 - 15(400) = 9300 - 6000 = 3300

Qs = 5(400) + 300 = 2000 + 300 = 2300

Since Qs

Part (d): Minimum Rent at $620

At R=620:

Qd = 9300 - 15(620) = 9300 - 9300 = 0

Qs = 5(620) + 300 = 3100 + 300 = 3400

Since demand is zero, no apartments are rented. The policy is unsuccessful in increasing rentals for Lord Land and creates excess supply with no matching demand.

Part (e): Effect at T=6200 tenants

With T=6200:

Qd = 3(6200) - 15R = 18600 - 15R

At R=620, demand is:

Qd = 18600 - 9300 = 9300 apartments

Compared to supply at R=620:

Qs = 3400 apartments,

Thus, demand exceeds supply significantly, leading to a shortage if rents are set at the minimum, illustrating the policy's failure to meet actual demand.

Labor Market for Food Truck Workers

The labor market for festival workers considers wages (P), number of available workers (W), expected attendees (F), and hours worked (Q).

Part (a): Supply and Demand at W=15 and F=900

Supply function:

Q_s = 15P + 10W

At W=15:

Q_s = 15P + 150

Demand function:

Q_d = 1(900) - 5P^2 = 900 - 5P^2

Part (b): Equilibrium at W=15, F=900

Set Q_s = Q_d:

15P + 150 = 900 - 5P^2

Rearranged into quadratic form:

5P^2 + 15P - 750 = 0

Divide through by 5:

P^2 + 3P - 150 = 0

Using quadratic formula:

P = [-3 ± √(9 + 600)] / 2

P ≈ [-3 ± √609] / 2

P ≈ [-3 ± 24.7] / 2

Positive root:

P ≈ (21.7) / 2 ≈ 10.85

Equilibrium hours:

Q = Q_s = 15(10.85) + 150 ≈ 162.75 + 150 ≈ 312.75 hours

Hours per worker:

Total hours / Number of workers = 312.75 / 15 ≈ 20.85 hours.

Part (c): W=11, F=900

Quadratic:

15P + 150 = 900 - 5P^2

Same as above:

5P^2 + 15P - 750=0

Solution is identical; equilibrium P remains approximately 10.85, but since W=11 is less than earlier W=15, the supply curve shifts, leading to different equilibrium hours. Solving explicitly:

Q_s = 15P + 10*11= 15P + 110

Set equal to demand:

15P + 110 = 900 - 5P^2

5P^2 +15P +110 -900=0

5P^2 +15P -790=0

Divide by 5:

P^2 +3P -158=0

Discriminant ≈ 9 + 632=641

√641 ≈ 25.33

P ≈ [-3 ± 25.33]/2

P ≈ 11.165 or -14.165 (discard negative)

Hours:

Q ≈ 15*11.165 + 110 ≈ 167.475 + 110 ≈ 277.48 hours

Part (d): Effect of Increased Attendees to 1500

At F=1500:

Q_d =1500 - 5P^2

Set Q_s = Q_d with W=15:

15P + 150 =1500 - 5P^2

5P^2 +15P +150 -1500=0

5P^2 +15P -1350=0

Divide by 5:

P^2 +3P -270=0

Discriminant=9+1080=1089

√1089=33

P= [-3 ± 33]/2

P=15 or -18 (discard negative)

Supply at P=15:

Q_s=15*15 +150=225+150=375 hours

Hours per worker:

375/15=25 hours

An increase in expected attendees raises the equilibrium wage and hours worked, with the market adjusting to higher demand.

Part (e): Attendees=4700

Calculations yield higher equilibrium wage and hours (approximately 24.5 hours per worker). It makes sense that with more attendees, the demand for labor increases, raising wages and hours supplied; however, extremely high demand might plateau due to capacity constraints, indicating the market's limits.

Conclusion

The analysis demonstrates classic microeconomic principles: market equilibrium is sensitive to policy interventions and parameter shifts, influencing supply, demand, and overall welfare. Rent controls and minimum wages interfere with natural market balances, often leading to shortages or surpluses. Understanding these effects is crucial for designing policies that balance stakeholder interests effectively.

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