Supply And Demand As Well As Consumer Behavior

Supply And Demand As Well As Consumer Behavior

This assignment covers supply and demand as well as consumer behavior. Please answer the questions below, which are related to Chapters 2 through 4 of P&R. Beyond reviewing the material from class, the problem sets are intended to develop the ability to apply the concepts from class to new situations. You are encouraged to collaborate with others, to research sources outside of class, and to ask questions during office hours. However, you must write up your responses individually. You should explain all of your answers in detail. Your score will depend on both the correctness of your solutions and the completeness of your explanations. Please write the question number next to your answer for each question. Your answers to the assignment are due in class on Thursday, September 22. Late assignments may be penalized.

Paper For Above instruction

Supply and Demand and Consumer Behavior: An Analytical Perspective

The interconnected concepts of supply, demand, and consumer behavior form the foundation of microeconomic theory, providing insights into how markets function and how prices and quantities are determined. This paper explores these fundamental principles, applying them to specific scenarios to enhance understanding and illustrate their practical implications.

1. Supply and Demand for Potatoes and Consumer Income Effects

The supply function for potatoes is given by QS = 2000 + 200P, and the demand function is QD = 4000 – 300P – 2I, where P is price and I is income. Given I = 500, several aspects are examined. Firstly, the demand function includes the variable I, indicating income’s effect on demand. As demand decreases with increasing I, potatoes can be classified as an inferior good; typically, superior goods see demand increase with income, but here, demand decreases as income increases, confirming their status as inferior goods.

Next, to find the equilibrium price and quantity, set QD = QS:

4000 – 300P – 2(500) = 2000 + 200P

4000 – 300P – 1000 = 2000 + 200P

3000 – 300P = 2000 + 200P

1000 = 500P

P = 2

Substitute P back into either supply or demand:

QS = 2000 + 200(2) = 2400

Therefore, the equilibrium price is $2, and the equilibrium quantity is 2400 units.

The price elasticities of demand and supply at equilibrium quantify responsiveness. Price elasticity of demand (Ed) is calculated as:

Ed = (dQd/dP) (P/Qd) = –300 (2/2400) = –0.25, indicating inelastic demand.

Price elasticity of supply (Es) is:

Es = (dQs/dP) (P/Qs) = 200 (2/2400) ≈ 0.167, also inelastic.

A government-imposed price support at P = 4 involves the government paying four dollars for each unsold potato. The quantity demanded at P = 4 is:

Qd = 4000 – 3004 – 2500 = 4000 – 1200 – 1000 = 1800

Supply at P = 4:

Qs = 2000 + 200*4 = 2000 + 800 = 2800

Since Qs > Qd, the excess supply is 1000 units. The government purchases the surplus of 1000 units at P = 4, and the quantity sold in the market is 1800 units.

2. Copper Market Equilibrium and Elasticities

Given the initial equilibrium at P = 5 and Q = 20, with demand elasticity of –0.5 and supply elasticity of 1.0, it is evident that demand is inelastic (|Ed|

Assuming linear demand and supply curves, we can derive their equations from the elasticities. The demand curve, with elasticity at equilibrium, is:

Ed = (dQ/dP) * (P/Q) = –0.5

Rearranged, dQ/dP = –0.5 (Q/P) = –0.5 (20/5) = –2

Thus, demand slope is –2, and demand equation: Qd = a – 2P. To find 'a', plug in equilibrium:

20 = a – 2*5 → a = 30

Demand curve: Qd = 30 – 2P.

Similarly, for supply:

Es = (dQ/dP) * (P/Q) = 1.0

Rearranged: dQ/dP = 1.0 (Q/P) = 1.0 (20/5) = 4

Supply slope: 4, with the form Qs = b + 4P. Solving for 'b' at equilibrium:

20 = b + 4*5 → b = 0

Supply curve: Qs = 4P.

When supply drops by 50%, the new supply function becomes Qs' = 0.5 * 4P = 2P. To find the new equilibrium, set demand equal to the new supply:

30 – 2P = 2P → 30 = 4P → P = 7.5

New equilibrium quantity: Q = 4 * 7.5 = 30.

Remaining demand at P = 7.5 is:

Qd = 30 – 2 * 7.5 = 15.

Thus, the new equilibrium price is $7.50, and the equilibrium quantity is 30 units.

Elasticities at the new equilibrium:

Ed = (dQ/dP) (P/Q) = –2 (7.5/15) = –1.0, elastic demand.

Es = 4 * (7.5/30) = 1.0, elastic supply.

3. Utility Functions of Pierre and Marie

Pierre's utility function is U(F,C) = 10FC. For utility level U = 10:

10 = 10FC → FC = 1

Any combination of F and C satisfying FC = 1 yields utility 10. The indifference curve is thus all baskets where the product of food and clothing equals 1. The curve can be plotted with points like (F, 1/F), illustrating a hyperbola.

Marie’s utility function is V(F,C) = 20F²C². For utility level V = 20:

20 = 20F²C² → F²C² = 1 → FC = 1

This is identical to Pierre’s indifference condition, meaning both have the same sets of baskets where FC = 1, but their preferences differ in intensity, with Marie's utility depending quadratically on both goods' quantities compared to Pierre's linear dependence.

The change in Pierre’s utility function to W(F,C) = 20FC² introduces a different curvature, emphasizing clothing more heavily. The indifference curve for W with a utility level of, say, 10, becomes F * C² = 0.5, which differs from the previous hyperbola, indicating altered preferences with a nonlinear focus on clothing.

4. Amelia’s Travel Utility and Budget Constraints

Amelia's utility is U(D,F) = 10DF, with prices $100 for D and $400 for F, and total income $4000. The budget constraint exhausts all income:

100D + 400F = 4000

The set of market baskets is all (D,F) satisfying this equation, which can be graphed as a straight line with intercepts at D = 40 and F = 10.

For utility level U = 1000:

10DF = 1000 → DF = 100

This hyperbolic indifference curve contains points where the product DF = 100. Plotting the curve involves solving for F in terms of D: F = 100 / D, and plotting it along with the budget line, which will intersect with this hyperbola at the optimal point.

The marginal rate of substitution (MRS) of D for F is the ratio of marginal utilities:

MRS = (∂U/∂D) / (∂U/∂F) = (10F) / (10D) = F / D

At the utility-maximizing point, this equals the price ratio:

F / D = 100 / 400 = 0.25

Thus, at optimality, F = 0.25 * D. Substituting into the budget constraint:

100D + 400(0.25D) = 4000 → 100D + 100D = 4000 → 200D = 4000 → D = 20

F = 0.25 * 20 = 5

5. Oscar’s Demand and Total Expenditure Analysis

Demand function: Q = 10 – 2P. The elasticity at P = 2 is:

Ed = (dQ/dP) (P/Q) = –2 (2/ (10 – 22)) = –2 (2/6) = –2 * (1/3) ≈ –0.6667, inelastic demand.

At P = 3, quantity demanded is:

Q = 10 – 2*3 = 10 – 6 = 4

Total expenditure (TE) at P=3:

TE = P Q = 3 4 = 12

Consumer surplus is the area of the triangle between the demand curve and the price line, up to the maximum willingness to pay (intercept at P = 5):

Maximum quantity at P=0: Qmax = 10, so consumer surplus = 0.5 (Qmax – Q) (Pmax – P) = 0.5 (10 – 4) (5 – 3) = 0.5 6 2 = 6.

The price that maximizes Oscar’s total expenditure occurs at the point where elasticity equals –1 (unit elastic). Since Ed = –2P / Q, setting |Ed|=1:

1 = 2P / Q → Q = 2P. Recall from demand: Q = 10 – 2P. Equate:

10 – 2P = 2P → 10 = 4P → P = 2.5.

At P = 2.5, Q = 10 – 22.5 = 10 – 5 = 5, and TE = 2.5 5 = 12.5.

Elasticity at this point is exactly –1, confirming maximum expenditure.

When price increases from 1 to 2:

Q at P=1: 8, TE=1*8=8; at P=2: 6, TE=12; expenditure rises.

From P=3 to 4:

Q at P=3: 4, TE=12; at P=4: 2, TE=8; expenditure falls.

6. Brian’s Utility Maximization with Water and Coffee

Utility: U(X,Y) = X + 16Y; prices PX=1, PY=4; income I varies.

At I=8: Budget line: X + 4Y = 8. The utility is maximized by allocating spending to the good with the highest marginal utility per dollar. Since MUx=1, MUY=16, and PY/PX=4, the ratio MUY/ PY=4, MUx/ PX=1. Because MUY/ PY > MUx/ PX, it is optimal to spend all income on Y until budget exhausted:

4Y = 8 → Y = 2; then X = 8 – 4*2 = 0. The optimal bundle: (X, Y) = (0, 2).

The marginal utility of income at I=8 is the increase in utility per additional dollar, which is proportional to MUx and MUY; since all income goes to Y, MU of income is effectively MUY/PY=16/4=4.

At I=32: Budget line: X + 4Y= 32. Same logic applies, allocate all income to Y:

4Y=32 → Y=8; then X=0. The optimal bundle: (X, Y)=(0,8). The marginal utility of income remains 4 units of utility per dollar invested in Y.

7. Personal Reflection on Studying Economics

While this is a personal question, a suitable response would be: "Studying economics allows me to understand how individuals and societies make decisions about resource allocation. It helps me analyze real-world issues like market dynamics, public policies, and global markets. With an economics degree, I hope to contribute to policies that promote economic stability and growth, and to solve pressing problems related to inequality and sustainable development." This explanation underscores the broad applicability and societal relevance of economics.

References

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