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Homework answers / question archive / After paying for rent and other necessities Emma has a budget (I) of 100 kronor each week that she can choose how to allocate between food (F) and entertainment (E)

After paying for rent and other necessities Emma has a budget (I) of 100 kronor each week that she can choose how to allocate between food (F) and entertainment (E)

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After paying for rent and other necessities Emma has a budget (I) of 100 kronor each week that she can choose how to allocate between food (F) and entertainment (E). Assume that the price of F (PF) is 10 kronor per unit and the price of E (PE) 10 kronor per unit. Assume that her utility function is given by ?=√?∗?.
Q1) c) Assume that her budget increases to 200 kronor each week. Draw the new budget constraint. For this particular utility function (Cobb-Douglas) demand for F is given by 0.5*I / PF (see GLS page 131-135 for a derivation) and equivalently for E. How much E and F will she consume at this higher income? What is her utility level?  
Q2) d) Keep I at 100 and PF at 10 kronor. Draw budget constraints and the optimal consumption of E for a number of different prices of E (using the optimal demand formula in d)). Use the same points to graph Emma's demand function for E. EDIT:
Cobb-Douglas utility maximization function: U (X, Y) = X^a* Y^1-a, where 0<a<1, and whose income is I = PxX+PyY.
For d) I don't know actually. It might be MRSxy = MUx/MUf.
Background information:
Seminar 2
2.1 Demand for refrigerators is increasing in many developing countries (see for instance Wolfram, Shelef, and Gertler (2012) "How will energy demand develop in the developing world?" Journal of Economic Perspectives.) [1] You're working for the refrigerator producer Kamet in India and you have results from two statistical studies. The first on the aggregate demand for refrigerators (lumping together all brands) and the second specifically studies demand for Kamet's top of the line model called Kelvin, and its close competitors. 
a)            The first study estimates that the income elasticity of demand for refrigerators in India is 0.8. If incomes were to increase by 5 percent by how much do we expect demand for refrigerators to increase? 
b)            In the same study the own-price elasticity for refrigerators is estimated to be -0.5. If prices fall by 10 percent, by how much do we expect demand to change. 
c)            The second study estimates the own-price elasticity of demand for Kelvin to be -4.5. How much less of Kelvin do you expect to sell if you raise the price by 10 percent?
d)            We expect that the own price elasticity of aggregate demand for refrigerators to be less elastic than the product specific own price elasticity of demand. Why? 
e)            The closest competitor to Kelvin is Celcius. The cross-price elasticity of demand for Kelvin with respect to the price of Celcius is 0.4. If the price of Celcius were to increase by 10 percent, what would happen to demand for Kelvin?  
 2.2 There has been considerable interest in understanding if demand for biofuel (ethanol) has contributed to higher prices of food (see for instance the introduction to Roberts and
 Schlenker, 2013, "Identifying Supply and Demand Elasticities of Agricultural Commodities: Implications for the US Ethanol Mandate, American Economic Review). 
Use Q to denote quantity and P price in kronor. The demand for corn can be divided into demand from buyers who seek to use corn for food and those who seek to use it for biofuel.
Let's say that the food demand for corn is given by 
Qfood = 18 - P
Demand for corn for biofuel production is given by:
Qbiofuel = 6 - 2P
a)    Draw the market demand for corn in a diagram with price on the vertical axis (market demand is in this case given by the sum of demand for food and for biofuel production).
b)   Assume that the price of corn is 2 kronor. What is the own-price elasticity of demand for corn? What is the own-price elasticity of food demand for corn and the own-price elasticity of biofuel demand for corn evaluated at 2 kronor? 
2.3 After paying for rent and other necessities Emma has a budget (I) of 100 kronor each week that she can choose how to allocate between food (F) and entertainment (E). Assume that the price of F (PF) is 10 kronor per unit and the price of E (PE) 10 kronor per unit. 
a) Draw Emma's budget constraint. If she buys 5 units of E, how much F can she afford?
b) Assume that her utility function is given by =√ ∗ Draw the indifference curve that corresponds to a utility level of 5 in the same diagram as a).
c) Assume that her budget increases to 200 kronor each week. Draw the new budget constraint. For this particular utility function (Cobb-Douglas) demand for F is given by 0.5*I / PF (see GLS page 131-135 for a derivation) and equivalently for E. How much E and F will she consume at this higher income? What is her utility level? 
d) Keep I at 100 and PF at 10 kronor. Draw budget constraints and the optimal consumption of E for a number of different prices of E (using the optimal demand formula in d)). Use the same points to graph Emma's demand function for E.
2.4 Oscar is indifferent between living in Stockholm and London (his indifference curves are independent of his location). Assume that he only consumes two goods and that the relative price of these goods differ between Stockholm and London. His employer offers a wage in London such that he would be able to afford the same consumption basket in London as he would in Stockholm. Would he achieve the same, higher or lower utility in London than in Stockholm if we assume that his basket in Stockholm was chosen optimally? Explain using a figure with indifference curves and budget lines
  

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