Question

4) Assume that you are consuming Pepsi and Coke only and you consider them as perfect substitute one can of Pepsi for one can of Coke. Assume that the price of Pepsi is $1 per can and price of Coke is $3 per can and that your income is $30. a) Draw the budget constraint and indifference curve as needed. b) Show the optimal consumption bundle on your graph. c) Now assume that price of Pepsi increase to $2. What would be the optimal consumption bundle then? What is the intuition? d) Now assume price for a can of Pepsi increases to $4. What would be the optimal consumption bundle? What is the income effect and substitution effect? 4.13 Suppose that George is interested in only two goods, cigars and scotch. Employ the indifference curve/budget line apparatus to show a case where a decrease in the price of cigars leads to an increase in George's scotch consumption. Does this imply that cigars and scotch are complements to George? Explain your answer. 4.14 Repeat the preceding question but assume that a decrease in the price of cigars leads to a decrease in George's scotch consumption. Does this imply that scotch is an inferior good in George's case? 4.15 Left and right shoes are perfect complements for most people. If only the price of right shoes increased, what would be the substitution effect of such a price change on the typical consumer's consumption of right shoes? (Assume that the only two goods that the consumer cares about are right and left shoes.) What about the income effect?

Answer 1

& Pepsi and Coke an elechstime goods, suppose x = pepsi (quartiny) X2 = coke (quantity) The utility function is given by :- 0LX,-*,) = x + x2 Puica of x = $1 =P Pelice of x2 = $3 = P2 money of cousunun = m = $30 a) the budget line pixit Pz X₂ = m. 11x + 3n₂ = 30 1 suppose X₂ 10 o 20 fiIC, his here Ic, Chigher satisfaction) supe of budget lime = -1 (30_o) 10 20 30 slope of indifference care a for given fonction, there are two indifference function camera and consumption at 10,10) for Ico and ( 30,o] for Ich. The consumer can go on consuming from Icohill, teaches ic, which gives move sah's fication and higher writity of 30. The love at (30,0) U= 30t0 = 30 ( consuming only x)

Intuitiully, a consumou will only consume x, as it's perica is lower than price of good X2. New c) The price of good x, = $2. new budget line : 2x, + 3x2 = 30 kq ↑ Suppose X2 10 20 - 15 - Zlo (5.o) The slope of budget lime =-110.10) 10 I30, Chisher Satisfaction) There are two indifference come an Ilo and IC, and o o is 20 m two consumption bundle are (0,10) and (15,0) The ceptional consumption handle is U=Xitxz U,= od 10 =10 2) U2 = 15 to = 15 this is optimal gines higher utility . The good with lower puice is cous und because good I is substituted with good l ie. Pepsi Scanner

du. 4x1+ 3 X2 =30 • d) The new pepsi perice is The new budget line is Surpose • x2 10 o - Similarly like abou • pauts. 10,10) Chishe catisfaction) • The Whility is given by U=xit x2 u = 7.5 to 7.5 os (454) io is 20 Uz= of 10 = 10 . 10376, therefore consumen will only bey good 2 - with low price x for • • • U21 Income and Substitution Effect . old price of Xi = $2 New puice of xy = $4 The pencil shows old and www budgel line and the blue line shows old and no in difference cene. The eaulice consuplich bevalle is not captional now Cousenu will shift to consumption at 10,10). As puice elf xi una cars, cariswer substihute Pepsi with coke. Income effect is ZERO

(scotch) N27 4.13 As seen in diagram cauler George was cousung ni units of cigan and uz crits of scotch at puice Prand na perice Pz euspectivity As puic of cigan falls, the budget live shifts outwards from non capaus in I, Iy to 1, I2. We can see with shift in perice, quantity of scotch inacases. This shows the two goods are COMPLEMENT as their cross-puice elasticath Scanned with CâmSpontine .

4.14 Yes, scotch is an infercor good in this case. Inferior goods occur when purchasing power (mony, of consumen increases and it eus ulls in fall in a demand for that good. So, decrease in puice of cigan increases the incour of consumer and leads to fall in demand for scotch and consuun will shift this demand to quality products CS CamScanner Scanned with

4.15 Complementary goods are consumed in a fixed proportion and together. The utility function of complementary goods is given by U = min{x1,x2}, where x1= good 1 and x2 = good 2.

The consumption are complementary good occurs at kink where indifference curve and budget line meet. The indifference curve is L-shaped curve. When price of one good increases, the purchasing power of the consumer falls resulting in less demand of goods by consumer. The indifference curve shifts inwards. That is Income Effect is valid in complementary goods.

However, the goods cannot be substituted for one another. Therefore at given level of income, the increase in price will have no effect on indifference curve.

Hence the substitution effect is 0 and income effect exists in case of complementary goods.