a. Budget Line is basically all those combinations of two goods, which the consumer can buy spending his given money income on the two goods at their given prices.
It can be written as
"BL= P_c \\times Q_c+ P_d \\times Q_d \\\\\n\n120= 1 \\times Q_c + 1 \\times Q_d \\\\\n\n120= Q_c + Q_d"
Budget line will be 120.
b. As the price of both the goods i.e. carrot and donuts is $1. They are perfect substitute for each other. The IC curve will be a straight line with negative slope because the marginal utility is constant. The value of this slope is throughout minus 1, and MRScd=1
So, IC curve will satisfy this equation
"\\frac{MU_c}{MU_d}= \\frac{P_c}{P_d} \\\\\n\nMU_c = Q_c \\\\\n\nMU_d= Q_d \\\\\n\n\\frac{Q_c}{Q_d}= \\frac{1}{1} \\\\\n\n\\frac{Q_c}{Q_d} = 1"
c. From a we can derive the budget line
"120= Q_c + Q_d \\\\\n\n120= Q_c + Q_c \\\\\n\n120 = 2Q_c \\\\\n\nQ_c = 60 \\\\\n\nQ_d= Q_c = 60"
So 60 units of both the goods will satisfy the Donald’s utility.
d. Given the budget line
"120= P_c \\times Q_c+ P_d \\times Q_d \\\\\n\n120= P_c \\times Q_c+ 1 \\times Q_d\n\nAs Q_d= Q_c\n\n120= P_c \\times Q_c+ 1 \\times Q_c \\\\\n\n120= Q_c(P_c+1)"
So quantity demanded
"Q_c = \\frac{120}{P_c+1}"
e. After the tax the price of donut will become $2. This will change IC curve. The new IC curve will be
"\\frac{MU_c}{MU_d}= \\frac{P_c}{P_d} \\\\\n\n\\frac{Q_c}{Q_d}= \\frac{1}{2} \\\\\n\nQ_c=2Q_d"
Now putting it into budget line
"120= P_c \\times Q_c+ P_d \\times Q_d \\\\\n\n120= 1 \\times Q_c+ 2 \\times Q_d \\\\\n\n120= 2 \\times Q_d+2 \\times Q_d \\\\\n\n4Q_d=120 \\\\\n\nQ_d=30 \\\\\n\nQ_c= 120-2 \\times 30 = 120- 60 = 60"
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