A commuter\'s utility function for gas (x-axis) and doughnuts (y-axis) is u(g,d)

Question

A commuter's utility function for gas (x-axis) and doughnuts (y-axis) is u(g,d)gd with MRS. His demand ida for gas is g27 Prices and income are currenty Ps 2, P2, and I 12, so at the moment he's consuming gold 3 gallons of gas and dol3. Next suppose (due to new oil discoveries), the price of gas falls to pe1. Use an indifference curve/budget diagram like those from class and the textbook to show the income and substitution effects of this price change on doughnut consumption. Compute the size of these two effects, discuss why they are positive or negative, and discuss how they relate to the total change in doughnut consumption, dnew- dold 2pg

Explanation / Answer

Substitution effect shows the inverse relationship between price and quantity demanded that means as price rises then quantity demanded decreases and as price falls then quantity demanded rises.

Income effect shows that as price increases then the real money demanded decreases which result in the less spending by the household because of a fall in the income of a consumer.

At equilibrium

MRSgd = Pg/ Pd

D/G = 1/2

2D = G

Budeget constraints

Pg.G + Pd. D =MY

1.G + 2.D = 12

G + 2.G/2 =12

G = 6

Put G=6 in equation of 2D=G

D = G/2

D = 6/2

D = 3

When price falls from 2 to 1 then the quantity demanded increases from 3 to 6 gallon shows the substitution effect which is always negative.

As the price decreases of a gallon than the purchasing power of the consumer increases and the demand for more quantity increases.

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