question_answer

Write a budget line equation of a consumer if the two goods purchased by the consumer Good X and Good Y are priced at Rs. 10 and Rs. 5 respectively and the consumer's income is Rs. 100.

Or

Define marginal rate of substitution. Explain its behaviour along an indifference curve.

 

Answer:

Let?s take           Price of Good X \[{{P}_{1}}\]

Price of Good Y \[{{P}_{2}}\]

Consumer?s income = Y

according to the sum -

\[{{P}_{1}}\] = Rs 10, \[{{P}_{2}}\]=Rs 5

Y = Rs 100

hence budget equation is -

\[{{P}_{1}}\,\,{{X}_{1\,\,}}+\,\,{{P}_{2\,\,}}{{X}_{2\,\,}}=\,\,Y\]

\[10{{X}_{1\,\,}}+\,\,5{{X}_{2\,\,}}=\,\,100\]

Or

Marginal Rate of Substitution (MRS).

MRS is the rate at which the consumer is ready to sacrifice some amount of good 1 for obtaining one more unit of his another good 2 without affecting his total utility.

For example a consumer has a bundle of two goods, say, \[2x+10y\] and shifts to another bundle of \[3x+6y\] maintaining the same level of satisfaction (total utility).

Here, MRS is \[4(106)\]units of y which the consumer is willing to giving up to obtain an extra unit of \[x=(3x2x).\] It can also be illustrated with the help of the figure.

The two points A & B are taken on IC curve. At point A, a consumer gets combination of OR (= MA) of good y and OM (= RA) of good. X. Suppose he shifts from point A to point B where he gets combination of OS (= MC) of good y and ON (= SB) of good X. By this change, he loses AC (MA ? MC) a maint of good y and gains CB (ON ? OM) amount of good X which means he is willing to substitute good X for goods y.

The slope of MRS can be understood as -

\[\frac{\Delta \,\,good\,\,y}{\Delta \,\,good\,\,x}\]