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