Answer to Question #263887 in Microeconomics for lily

Question

Jose consumes only good A and good B. His utility function is C (A, B) = 4AB + 20. The price of good A is $4, but if Jose consumes more than 10 units of good A, the price is $1 higher. The price of good B is constant at $2 and his income is constant at $400. [25%]

a. Formulate Jose’s budget constraint and explain how his budget set changes when he consumes more than 10 units of good A.

b. Refer to the budget constraint in (a). Explain how Jose’s optimal choice and wellbeing change.

c. What other strategies that the government could use to control the consumption of good A? Use a diagram or a budget constraint function to explain one strategy.

d. Does the policy in (c) make Jose worse off? Discuss.

Answer 1

The given information says,

Good A & Good B are consumed by Jose,

Constant Income = $400 = I

Unit Price of Good A = $4 = Pa

{at consumption > 10 units, price increases by $1}

Unit Price of Good B = $2 = Pb

Utility Function: C (A, B) = 4AB + 20.

(а) (i) So, the Jose's budget constraints— Before changes

Pa*A + Pb*B = I

Function: $400 = 4*A + 2*B

400 = 4A + 2B

B = (400 - 4A)/2

B = 200 - 2A -----(eq)

Graphical representation of Budget Constraint—

A on Horizontal Axis; B on Vertical Axis

(а) (ii) Jose's budget constraints— After changes

Changes: At consumption of Good A >10 units, price increases by $1

Thus,

Function: $400 = 5*A + 2*B [If A>10 units]

400 = 5A + 2B

B = 200 - (5/2)A-----(eq2)

Graphical representation of change in Budget Constraint—

(1) (ii) Jose's budget constraints— After changes

Changes: At consumption of Good A >10 units, price increases by $1

Thus,

Function: $400 = 5*A + 2*B [If A>10 units]

400 = 5A + 2B

B = 200 - (5/2)A-----(eq2)

Graphical representation of change in Budget Constraint—

A on Horizontal Axis; B on Vertical Axis

(b) Refering to the budget constraint drawn above,

Understanding Jose’s optimal choice and wellbeing change—

Jose's optimal choice must be the amount of Good A&B purchased optimally. To be more clear, optimal choice is purchasing a set of both goods, in a manner, that increases and maximizes Jose's satisfaction, within his budget constraint.

Optimal Choice or Optimal Consumption is plotted on the budget line.

Given, Utility Function: C (A, B) = 4AB + 20

380 = 4AB

380/4A = B

95/A = B

Maximizing Utility: Max C(A,B)

Subject to: Pa*A + Pb*B ≤ I

"Pa*A + Pb*B ≤ I" denotes that, spending on consumption doesn't exceeds Income.

I = $400 per month, the price of Good A is Pa = $4/unit, and the price of Good B is Pb = $2/unit.

At budget line, vertical intercept at y = 200, indicating that if Jose spend all his income on Good A, he could buy 200 units of Good A. Similarly, the horizontal intercept at x = 100 shows that Jose could buy 100 units of Good B, on spending all his income on Good B.

Thus, The slope of the budget line is −Pa /Pb = –2

Now Plotting Indifference curves U1, U2, and U3 on graph to identify maximum utility.

Indifference curve that lies on the budget constraint, and satisfies the slope is optimal choice for Jose.

Thus at U2, utility is maximum.

(c) To restrict the consumption of Good A, Government should implement a price policy, in which, a consumer has to pay two times the actual price on purchase of 10 units.

Effect of the above strategy on Budget Constraint of Jose—

2×APa + BPb = $400 {consuming more than 10 units of Good A}

2*A*4 + B*2 = 400

8A + 2B = 400

B = 200 - 4A

(d) Jose's Budget Constraint after Policy in (c) had a drastic changes, his consumption of Good A reduced by half. Thus we can say, that Jose's position is worsen off, as compared to position before policy implementation.