Suppose that a consumer\'s preferences are well behaved in that properties 4-1 t

Question

Suppose that a consumer's preferences are well behaved in that properties 4-1 to 4-4 are satisfied and the initial budget constraint is given by 300 = 2X + 4Y. At the initial budget constraint, this consumer purchases 100 units of good X and 25 units of good Y. Suppose the price of X increases to $4 per unit, resulting in a new consumption bundle consisting of 60 units of X and 15 units of Y. Then, the slope of the inverse demand for good X over this consumption range is:

0.05.

0.05.

0.267.

0.444.

-0.05 IS CORRECT? WHY IS THIS CORRECT? PLEASE EXPLAIN STEP BY STEP

Explanation / Answer

Inverse demand function of good X:

Q = a - bP

When P = 2 [From initial budget constraint], Q = 100

So, 100 = a - 2b ..... (1)

When P = 4, Q = 60

60 = a - 4b .......(2)

(1) - (2) Gives u:

40 = 2b

b = 20

So, a = 100 + 2b [From (1)]

= 100 + 40 = 140

So inverse demand function:

Q = 140 - 20P

Or, 20P = 140 - Q

P = 7 - 0.05Q

Slope of the inverse demand function = dP / dQ = - 0.05

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.