Answer to Question #153027 in Microeconomics for talha ahmad khan

Question

Mr. X buys two goods: Pizza and chickenburgers. The price of a Pizza is Rs. 1, and the price of a chickenburgers is Rs. 2. Each month, Mr. X spends all of her income and buys 30 Pizza and 5 chickenburgers. Next month, the price of magnet will fall to Rs. 0.50 and the price of a chickenburger will rise to Rs. 5.
a) Draw the budget line.
b) Will Mr. X able to buy 30 pizza and 5 chicken burgers next month?
c) Will Mr. X want to buy 30 pizza and 5 chicken burgers at new prices?
d) If at the new prices, Mr. X marginal utility of another pizza is 40, and the marginal utility of another chickenburger is 80. Is Mr. X maximize the utility? If not, how can he maximize his utility?

Answer 1

P – pizza, C – chickenburgers

The price of a Pizza is Rs. 1

The price of chickenburgers is Rs. 2

The budget line is represented as:

Income(Y) = Price of pizza*Quantity of pizza + Price of chickenburger*Quantity of chickenburger

Y = 1P + 2C

For P=30 and C=5:

$Y = 1 \times 30 + 2 \times 5 \\ Y = 30+10 \\ Y =40$

The budget line:

40 = 1P + 2C

Next month, the price of Pizza will fall to Rs. 0.5 and the price of a chickenburger will rise to Rs. 5.

The budget line for next month:

Y = 0.50P + 5C

40 = 0.50P + 5C

a) draw the budget line, we need at least two points. Let us represent Pizza on the Vertical axis and Chickenburger on the Horizontal axis.

40 = 1P + 2C

P = 40 - 2C

If P = 0

$C =\frac{40}{2} =20$

If C = 0

P =40

The two points are (0,40) (20,0).

The Budget line:

b)

$P=30 \\ C=5 \\ Y = 0.50P + 5C \\ Y = 0.50 \times 30 + 5 \times 5 \\ Y = 15 + 25 \\ Y = 40$

Mr X's total income is 40. So, he will be able to buy 30 pizza and 5 chicken burgers next month.

c) As shown in the above part Mr X can buy 30 pizza and 5 chicken burgers. But the goal of Mr X will be to maximize his utility. He will buy this combination of pizza and chicken burgers only if it maximizes his utility.

d) Suppose marginal utility and price of pizza is denoted by MU_p and P_p and marginal utility and price of chickenburger MU_c and P_c.

For Utility Maximization:

$\frac{MU_p}{P_p} =\frac{MU_c}{P_c} \\ \frac{MU_p}{P_p} = \frac{40}{0.5} = 80 \\ \frac{MU_c}{P_c} = \frac{80}{5} = 16$

Since they are not equal. He will not choose this combination.

He can maximize his utility by changing the price of one of the goods. e.g, if the price of chickenburger reduces to 1, $\frac{MU_c}{P_c}$ will be equal to $\frac{MU_p}{P_p}$ , That is he will maximize his utility. But this decrease in price means ; $0.50 \times 30 + 1 \times 5 = 20$ . income spent will reduce by 20. The income will not be fully spent.