Question 1-9.docx - Economics Lesson Question 1(a We have U = F1/2C1/2 Budget Equation will be PFF PCC = Income i.e F C = 100 To Find the optimal demand

Question 1-9.docx - Economics Lesson Question 1(a We have U...

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Economics Lesson Question 1 (a)We have U = F 1/2 C 1/2 Budget Equation will be: P F F + P C C = Income i.e. F + C = 100 To Find the optimal demand, we need to equate MRS with price ratio MRS = (dU/dF)/(dU/dC) = ((1/2)F -1/2 C 1/2 )/ ((1/2)F 1/2 C -1/2 ) = C/F Price Ratio = P F /P C = 1 / 1 = 1 MRS = Price Ratio Gives: C/F = 1 i.e. C = F Substitute C = F in Budget Equation F + F = 100 2F = 100 F = 50 Since C = F, Thus, C = F = 50 So, (C, F) = (50, 50) SO, Consumer will buy 50 units of each.
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(b)Since 200 units of food is free, which would have otherwise costed 1*200 = 200 This is equivalent to giving income of 200 but with restriction that only food can be bought with it. So, if the quantity of food is greater than 200, we can treat 200 as additional Income i.e. F + C = 300 if F >= 200 For remaining portion, the budget constraint will be same as before i.e. F + C = 100 We can draw this as follows: Now, using the new constraint: F + C = 300 And Using MRS = Price Ratio condition, we get: F = C Substituting in Budget, we get: C + C = 300 2C = 300 C = 150 F = C = 150
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But since the subsidy is on food and not on composite goods, so, C cannot exceed 100 i.e. max value of C can be: Income/Price of C = 100/1 = 100 But he wants to purchase C = 150 which is not possible SO, C will be restricted to 100 and rest of the income will be spent on food i.e. if C = 100, we get: F + 100 = 300 F = 200 So, (F, C) = (200 , 100) is the new demand (c) This can be represented graphically as follows: Initial indifference curve was much lower than the new one. Thus, the household is better off with subsidy Initially Utility was, U = 50 1/2 50 1/2 = 50 New Utility, U = 200 1/2 100 1/2 = 141.42 Household is better by: 141.42 – 50 = 91.42 units of utility
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Here, we have assumed 1 utility = 1$. Thus, household is better off by 91.42 dollars Question 2 The budget line takes the form: P Gasoline *Q Gasoline + P Other_Goods *Q Other_Goods = Income Suppose income was initially 10000 and Price of other goods was 1, we get the budget equation as: 1*G + 1*C = 10000 i.e. G + C = 10000 After price hike and rise in income, budget equation becomes: 2G + C = 11000 Initially, the consumer was spending following on Gasoline: Quantity * Price = 1000*1 = 1000 After the hike, the consumer will be spending following on same quantity of Gasoline: Quantity *Price = 1000*2 = 2000 Excess money required to buy this: 2000 – 1000 = 1000 Excess money he got = 1000 So, he is still able to afford the initial combination goods but now since he has additional income, if he decided to buy less gasoline and more of other
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goods due to the substitution effect, he will be better off. This can shown as follows: Since he is not on higher IC, he is better off.
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