Answer to Question #303615 in Microeconomics for saanvi

Question

Draw a consumer budget constraint and indifference curves for Pepsi and Pizza. Find out the optimal consumption choice when consumer has income of $2000 and the price of Pepsi is $5 per bottle and the price of per pizza is $10.What is the marginal rate of substitution at this optimum?

Answer 1

Budget constraint:

Given: Two goods Pizza and Pepsi

In the below figure, the line AF shows the various combination of goods the consumer can purchase. This line is the budget line or budget constraint. It shows the possible combination of Pizza and Pepsi that a consumer can purchase given the prices of the goods and the income. These combinations are indicated by points A, B, C, D, E and F

Indifference curve:

In the below figure, we measure the quantity of Pizza along the X-axis and the quantity of Pepsi along the Y-axis. The consumer can buy different combinations of Pizza and Pepsi. Both these combinations are equally preferred, and the consumer is indifferent to these two combinations. When the scale of preference of the consumer is graphed by joining the points A, B, C, D, we obtain an Indifference curve IC.

Budget=$P_1× Q1_​ + P_2​× Q_2 ​$

$\$2000=\$5x+\$10y$

The marginal rate of substitution is given below

$|MRS_{xy}|=\frac{\delta y}{\delta x}=\frac{MU_y}{MU_x^{'}}$

$=\frac{MU_y}{MU_x^{'}}=\frac{-5}{-10}=0.5$