Answer to Question #223761 in Microeconomics for Tege

Question

Assume a hypothetical consumer consumes orange and banana. The price of orange is 2 and price of banana is 4 and the consumer budget is birr 20 for the two goods. Where: QX is quantity of orange, QY is quantity of banana and TUX and TUY is total utility from consuming orange and banana respectively.

Orange, Price=2birr

Banana, Price=4birr

Qx

TUx

MUx

MUx/Px

Qy

TUy

MUy

MUy/Py

1

6

1

6

2

10

2

22

3

12

3

32

4

13

4

40

5

13

5

45

6

11

6

48

Based on the given information, answer the following questions.

Compute the marginal utility of the of the two goods

At what amounts consumption does diminishing marginal utility starts to occur for the two goods?

Determine the quantities of the two goods that the consumer should buy in order to maximize his total utility?

When will the consumer be at equilibrium?

Answer 1

Solution:

a.). The marginal utilities have been derived as per the below table:

MU = $\frac{Change \; in \; Total \; Utility}{Change \; in \; Quantity}$

 

b.). Diminishing marginal utility for Qx starts at consumption = 2

Diminishing marginal utility for Qy starts at consumption = 3

 

c.). Budget constraint: I = PxX + PyY

20 = 2X + 4Y

At utility maximization, $\frac{MUx}{MUy} = \frac{Px}{Py}$

Or $\frac{MUx}{Px} = \frac{MUy}{Py}$

Oranges (Qx) = 2

Bananas (Qy) = 4

The quantities of the two goods that the consumer should buy in order to maximize his total utility are 2 and 4: Uxy = (2, 4)

 

d.). The consumer will be at equilibrium at the point where $\frac{MUx}{Px} = \frac{MUy}{Py}$

Therefore, at equilibrium, the consumer will purchase 2 Oranges and 4 bananas.